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Book description

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

Reviews

'… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.'

Arnaud Beauville Source: MathSciNet

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References
Abhyankar [1984] S., Abhyankar, “Combinatoire des tableaux de Young, variétés déterminantielles et calcul de fonctions de Hilbert”, Rend. Sem. Mat. Univ. Politec. Torino 42:3 (1984), 65–88.
Alexander and Hirschowitz [1995] J., Alexander and A., Hirschowitz, “Polynomial interpolation in several variables”, J. Algebraic Geom. 4:2 (1995), 201–222.
Altman and Kleiman [1970] A., Altman and S., Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Math. 146, Springer, Berlin-New York, 1970.
Aluffi [1990] P., Aluffi, “The enumerative geometry of plane cubics, I: Smooth cubics”, Trans. Amer. Math. Soc. 317:2 (1990), 501–539.
Aluffi [1991] P.|Aluffi, “The enumerative geometry of plane cubics, II: Nodal and cuspidal cubics”, Math. Ann. 289:4 (1991), 543–572.
Andreotti and Frankel [1959] A., Andreotti and T., Frankel, “The Lefschetz theorem on hyperplane sections”, Ann. of Math.. 2/ 69 (1959), 713–717.
Arbarello et al. [1985] E., Arbarello, M., Cornalba, P. A., Griffiths, and J., Harris, Geometry of algebraic curves, I, Grundlehren der Mathematischen Wissenschaften 267, Springer, New York, 1985.
Artin [1982] M., Artin, “Brauer–Severi varieties”, pp. 194–210 in Brauer groups in ring theory and algebraic geometry (Wilrijk, 1981), edited by A., Verschoren, Lecture Notes in Math. 917, Springer, Berlin-New York, 1982.
Atiyah [1957] M. F., Atiyah, “Complex analytic connections in fibre bundles”, Trans. Amer. Math. Soc. 85 (1957), 181–207.
Atiyah and Hirzebruch [1961] M. F., Atiyah and F., Hirzebruch, “Vector bundles and homogeneous spaces”, pp. 7–38 in Differential Geometry, edited by C. B., Allendoerfer, Proc. Sympos. Pure Math. 3, Amer. Math. Soc., Providence, RI, 1961.
Bădescu [2001] L., Bădescu, Algebraic surfaces, Springer, New York, 2001.
Barth [1975] W., Barth, “Larsen's theorem on the homotopy groups of projective manifolds of small embedding codimension”, pp. 307–313 in Algebraic geometry (Arcata, CA, 1974), edited by R., Hartshorne, Proc. Sympos. Pure Math. 29, Amer. Math. Soc., Providence, RI, 1975.
Barth [1977] W., Barth, “Moduli of vector bundles on the projective plane”, Invent. Math. 42 (1977), 63–91.
Barth et al. [2004] W., Barth, K., Hulek, C. A. M., Peters, and A. Van de, Ven, Compact complex surfaces, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 4, Springer, Berlin, 2004.
Bayer [1982] D., Bayer, The division algorithm and the Hilbert scheme, Ph.D. thesis, Harvard University, Ann Arbor, MI, 1982. Available at http://search.proquest.com/docview/303209159.
Bayer and Eisenbud [1995] D., Bayer and D., Eisenbud, “Ribbons and their canonical embeddings”, Trans. Amer. Math. Soc. 347:3 (1995), 719–756.
Beauville [1996] A., Beauville, Complex algebraic surfaces, 2nd ed., London Mathematical Society Student Texts 34, Cambridge University Press, 1996.
Beheshti [2006] R., Beheshti, “Lines on projective hypersurfaces”, J. Reine Angew. Math. 592 (2006), 1–21.
Beheshti and Mohan Kumar [2013] R., Beheshti and N., Mohan Kumar, “Spaces of rational curves on hypersurfaces”, J. Ramanujan Math. Soc.28A (2013), 1–19.
Bifet et al. [1990] E., Bifet, C. De, Concini, and C., Procesi, “Cohomology of regular embeddings”, Adv. Math. 82:1 (1990), 1–34.
Boissière and Sarti [2007] S., Boissière and A., Sarti, “Counting lines on surfaces”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6:1 (2007), 39–52.
Borel [1991] A., Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics 126, Springer, New York, 1991.
Borel and Serre [1958] A.|Borel and J.-P., Serre, “Le théorème de Riemann–Roch”, Bull. Soc. Math. France 86 (1958), 97–136.
Bott and Tu [1982] R., Bott and L. W., Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer, New York-Berlin, 1982.
Brambilla and Ottaviani [2008] M. C., Brambilla and G., Ottaviani, “On the Alexander–Hirschowitz theorem”, J. Pure Appl. Algebra 212:5 (2008), 1229–1251.
Brieskorn and Knörrer [1986] E., Brieskorn and H., Knörrer, Plane algebraic curves, Birkhäuser, Basel, 1986.
Brill and Noether [1874] A., Brill and M., Noether, “Über die algebraischen Functionen und ihre Anwendung in der Geometrie”, Math. Ann. 7 (1874), 269–310.
Buchsbaum and Eisenbud [1977] D. A., Buchsbaum and D., Eisenbud, “What annihilates a module?”, J. Algebra 47:2 (1977), 231–243.
Call and Lyubeznik [1994] F., Call and G., Lyubeznik, “A simple proof of Grothendieck's theorem on the parafactoriality of local rings”, pp. 15–18 in Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), edited by W. J., Heinzer et al., Contemp. Math. 159, Amer. Math. Soc., Providence, RI, 1994.
Caporaso and Harris [1998] L., Caporaso and J., Harris, “Counting plane curves of any genus”, Invent. Math. 131:2 (1998), 345–392.
Cavazzani [2016] F., Cavazzani, A geometric invariant theory compactification of the space of twisted cubics, Ph.D. thesis, Harvard University, 2016.
Ceresa and Collino [1983] G., Ceresa and A., Collino, “Some remarks on algebraic equivalence of cycles”, Pacific J. Math. 105:2 (1983), 285–290.
Chasles [1864] M., Chasles, “Construction des coniques qui satisfont à cinque conditions”, C. R. Acad. Sci. Paris 58 (1864), 297–308.
Chern [1946] S.-S., Chern, “Characteristic classes of Hermitian manifolds”, Ann. of Math. (2) 47 (1946), 85–121.
Chow [1956] W.-L., Chow, “On equivalence classes of cycles in an algebraic variety”, Ann. of Math. (2) 64 (1956), 450–479.
Ciliberto [1987] C., Ciliberto, “Hilbert functions of finite sets of points and the genus of a curve in a projective space”, pp. 24–73 in Space curves (Rocca di Papa, 1985), edited by F., Ghione et al., Lecture Notes in Math. 1266, Springer, Berlin, 1987.
Clebsch [1861] A., Clebsch, “Zur Theorie der algebraischen Flächen”, J. Reine Angew. Math. 58 (1861), 93–108.
Coșkun [2009] I., Coșkun, “A Littlewood–Richardson rule for two-step flag varieties”, Invent. Math. 176:2 (2009), 325–395.
Collino [1975] A., Collino, “The rational equivalence ring of symmetric products of curves”, Illinois J. Math. 19:4 (1975), 567–583.
Cools et al. [2012] F., Cools, J., Draisma, S., Payne, and E., Robeva, “A tropical proof of the Brill–Noether theorem”, Adv. Math. 230:2 (2012), 759–776.
Cox and Katz [1999] D. A., Cox and S., Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs 68, Amer. Math. Soc., Providence, RI, 1999.
Dale [1985] M., Dale, “Severi's theorem on the Veronese-surface”, J. London Math. Soc. (2) 32:3 (1985), 419–425.
De Concini and Procesi [1983] C. De, Concini and C., Procesi, “Complete symmetric varieties”, pp. 1–44 in Invariant theory (Montecatini, 1982), edited by F., Gherardelli, Lecture Notes in Math. 996, Springer, Berlin, 1983.
De Concini and Procesi [1985] C. De, Concini and C., Procesi, “Complete symmetric varieties, II: Intersection theory”, pp. 481–513 in Algebraic groups and related topics (Kyoto/Nagoya, 1983), edited by R., Hotta, Adv. Stud. Pure Math. 6, North-Holland, Amsterdam, 1985.
De Concini et al. [1980] C. De, Concini, D., Eisenbud, and C., Procesi, “Young diagrams and determinantal varieties”, Invent. Math. 56:2 (1980), 129–165.
De Concini et al. [1982] C. De, Concini, D., Eisenbud, and C., Procesi, Hodge algebras, Astérisque 91, Société Mathématique de France, Paris, 1982.
De Concini et al. [1988] C. De, Concini, M., Goresky, R., MacPherson, and C., Procesi, “On the geometry of quadrics and their degenerations”, Comment. Math. Helv. 63:3 (1988), 337–413.
Decker et al. [2015] W., Decker, G.-M., Greuel, G., Pfister, and H., Schönemann, “SINGULAR 4-0-2—A computer algebra system for polynomial computations”, 2015. Available at http://singular.uni-kl.de.
Dieudonné [1969] J., Dieudonné, “Algebraic geometry”, Advances in Math. 3 (1969), 233–321.
Donagi and Smith [1980] R., Donagi and R., Smith, “The degree of the Prym map onto the moduli space of five-dimensional abelian varieties”, pp. 143–155 in Journées de Géometrie Algébrique d'Angers (Angers, 1979), edited by A., Beauville, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.
Doubilet et al. [1974] P., Doubilet, G.-C., Rota, and J., Stein, “On the foundations of combinatorial theory, IX: Combinatorial methods in invariant theory”, Studies in Appl. Math. 53 (1974), 185–216.
Ein [1986] L., Ein, “Varieties with small dual varieties, I”, Invent. Math. 86:1 (1986), 63–74.
Eisenbud [1995] D., Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics 150, Springer, New York, 1995.
Eisenbud [2005] D., Eisenbud, The geometry of syzygies, Graduate Texts in Mathematics 229, Springer, New York, 2005.
Eisenbud and Harris [1983a] D., Eisenbud and J., Harris, “Divisors on general curves and cuspidal rational curves”, Invent. Math. 74:3 (1983), 371–418.
Eisenbud and Harris [1983b] D., Eisenbud and J., Harris, “A simpler proof of the Gieseker–Petri theorem on special divisors”, Invent. Math. 74:2 (1983), 269–280.
Eisenbud and Harris [1987] D., Eisenbud and J., Harris, “On varieties of minimal degree (a centennial account)”, pp. 3–13 in Algebraic geometry (Bowdoin, ME, 1985), edited by S. J., Bloch, Proc. Sympos. Pure Math. 46, Amer. Math. Soc., Providence, RI, 1987.
Eisenbud and Harris [1992] D., Eisenbud and J., Harris, “Finite projective schemes in linearly general position”, J. Algebraic Geom. 1:1 (1992), 15–30.
Eisenbud and Harris [2000] D., Eisenbud and J., Harris, The geometry of schemes, Graduate Texts in Mathematics 197, Springer, New York, 2000.
Eisenbud and Schreyer [2008] D., Eisenbud and F.-O., Schreyer, “Relative Beilinson monad and direct image for families of coherent sheaves”, Trans. Amer. Math. Soc. 360:10 (2008), 5367–5396.
Eisenbud et al. [1996] D., Eisenbud, M., Green, and J., Harris, “Cayley–Bacharach theorems and conjectures”, Bull. Amer. Math. Soc. (N.S.) 33:3 (1996), 295–324.
Eisenbud et al. [2003] D., Eisenbud, F.-O., Schreyer, and J., Weyman, “Resultants and Chow forms via exterior syzygies”, J. Amer. Math. Soc. 16:3 (2003), 537–579.
Fröberg [1985] R., Fröberg, “An inequality for Hilbert series of graded algebras”, Math. Scand. 56:2 (1985), 117–144.
Fulton [1984] W., Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 2, Springer, Berlin, 1984.
Fulton [1993] W., Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, Princeton University Press, 1993.
Fulton [1997] W., Fulton, Young tableaux, London Mathematical Society Student Texts 35, Cambridge University Press, 1997.
Fulton and Harris [1991] W., Fulton and J., Harris, Representation theory, Graduate Texts in Mathematics 129, Springer, New York, 1991.
Fulton and Lazarsfeld [1981] W., Fulton and R., Lazarsfeld, “On the connectedness of degeneracy loci and special divisors”, Acta Math. 146:3-4 (1981), 271–283.
Fulton and MacPherson [1978] W., Fulton and R., MacPherson, “Defining algebraic intersections”, pp. 1– 30 in Algebraic geometry (Univ. Tromso, 1977), edited by L. D., Olson, Lecture Notes in Math. 687, Springer, Berlin, 1978.
Fulton and MacPherson [1981] W., Fulton and R., MacPherson, Categorical framework for the study of singular spaces, Mem. Amer. Math. Soc. 243, Amer. Math. Soc., Providence, RI, 1981.
Fulton and Pandharipande [1997] W., Fulton and R., Pandharipande, “Notes on stable maps and quantum cohomology”, pp. 45–96 in Algebraic geometry (Santa Cruz, 1995), edited by J., Kollár et al., Proc. Sympos. Pure Math. 62, Amer. Math. Soc., Providence, RI, 1997.
Fulton et al. [1983] W., Fulton, S., Kleiman, and R., MacPherson, “About the enumeration of contacts”, pp. 156–196 in Algebraic geometry—open problems (Ravello, 1982), edited by C., Ciliberto et al., Lecture Notes in Math. 997, Springer, Berlin, 1983. van Gastel [1990] L. van, Gastel, “Excess intersections in projective space”, pp. 109–124 in Topics in algebra, II (Warsaw, 1988), edited by S., Balcerzyk et al., Banach Center Publ. 26, PWN, Warsaw, 1990.
Gelfand et al. [2008] I. M., Gelfand, M. M., Kapranov, and A. V., Zelevinsky, Discriminants, resultants and multidimensional determinants, Birkhäuser, Boston, 2008. Reprint of the 1994 edition.
Golubitsky and Guillemin [1973] M., Golubitsky and V., Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics 14, Springer, New York-Heidelberg, 1973.
Grayson and Stillman [2015] D., Grayson and M., Stillman, “Macaulay2: a software system for research in algebraic geometry”, 2015. Available at http://math.uiuc.edu/Macaulay2.
Grayson et al. [2012] D., Grayson, A., Seceleanu, and M., Stillman, “Computations in intersection rings of flag bundles”, preprint, 2012. Available at http://arxiv.org/abs/1205.4190.
Green [1989] M., Green, “Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann”, pp. 76–86 in Algebraic curves and projective geometry (Trento, 1988), edited by E., Ballico and C., Ciliberto, Lecture Notes in Math. 1389, Springer, Berlin, 1989.
Greuel et al. [2007] G.-M., Greuel, C., Lossen, and E., Shustin, Introduction to singularities and deformations, Springer, Berlin, 2007.
Griffiths and Adams [1974] P., Griffiths and J., Adams, Topics in algebraic and analytic geometry, Mathematical Notes 13, Princeton University Press and University of Tokyo Press, 1974.
Griffiths and Harris [1979] P., Griffiths and J., Harris, “Algebraic geometry and local differential geometry”, Ann. Sci. École Norm. Sup. (4) 12:3 (1979), 355–452.
Griffiths and Harris [1980] P., Griffiths and J., Harris, “On the variety of special linear systems on a general algebraic curve”, Duke Math. J. 47:1 (1980), 233–272.
Griffiths and Harris [1985] P., Griffiths and J., Harris, “On the Noether–Lefschetz theorem and some remarks on codimension-two cycles”, Math. Ann. 271:1 (1985), 31–51.
Griffiths and Harris [1994] P., Griffiths and J., Harris, Principles of algebraic geometry, Wiley, New York, 1994. Reprint of the 1978 original.
Grothendieck [1958] A., Grothendieck, “La théorie des classes de Chern”, Bull. Soc. Math. France 86 (1958), 137–154.
Grothendieck [1963] A., Grothendieck, “Eléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohÉrents, II”, Inst. Hautes Études Sci. Publ. Math. 17 (1963), 5–91.
Grothendieck [1966a] A., Grothendieck, “Le groupe de Brauer, I: Algèbres d'Azumaya et interprétations diverses”, in Séminaire Bourbaki 1964=1965 (Exposé 290), W. A., Benjamin, Amsterdam, 1966. Reprinted as pp. 199–219 in Séminaire Bourbaki 9, Soc. Math. France, Paris, 1995.
Grothendieck [1966b] A., Grothendieck, “Techniques de construction et théorèmes d'existence en géométrie algébrique, IV: Les schémas de Hilbert”, in Séminaire Bourbaki 1960=1961 (Exposé 221), W. A., Benjamin, Amsterdam, 1966. Reprinted as pp. 249–276 in Séminaire Bourbaki 6, Soc. Math. France, Paris, 1995.
Gruson and Peskine [1982] L., Gruson and C., Peskine, “Genre des courbes de l'espace projectif, II”, Ann. Sci. École Norm. Sup. (4) 15:3 (1982), 401–418.
Hamm [1995] H. A., Hamm, “Affine varieties and Lefschetz theorems”, pp. 248–262 in Singularity theory (Trieste, 1991), edited by D. T., et al., World Sci. Publ., 1995.
Harris [1979] J., Harris, “Galois groups of enumerative problems”, Duke Math. J. 46:4 (1979), 685–724.
Harris [1982] J., Harris, “Theta-characteristics on algebraic curves”, Trans. Amer. Math. Soc. 271:2 (1982), 611–638.
Harris [1995] J., Harris, Algebraic geometry, Graduate Texts in Mathematics 133, Springer, New York, 1995. Corrected reprint of the 1992 original.
Harris and Eisenbud [1982] J., Harris and D., Eisenbud, Curves in projective space, Séminaire de Mathématiques Supérieures 85, Presses de l'Université de Montréal, Quebec, Canada, 1982.
Harris and Morrison [1998] J., Harris and I., Morrison, Moduli of curves, Graduate Texts in Mathematics 187, Springer, New York, 1998.
Harris et al. [1998] J., Harris, B., Mazur, and R., Pandharipande, “Hypersurfaces of low degree”, Duke Math. J. 95:1 (1998), 125–160.
Hartshorne [1966] R., Hartshorne, “Connectedness of the Hilbert scheme”, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5–48.
Hartshorne [1974] R., Hartshorne, “Varieties of small codimension in projective space”, Bull. Amer. Math. Soc. 80 (1974), 1017–1032.
Hartshorne [1977] R., Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer, New York-Heidelberg, 1977.
Hassett [2007] B., Hassett, Introduction to algebraic geometry, Cambridge University Press, 2007.
Herzog and Trung [1992] J., Herzog and N. V., Trung, “Gröbner bases and multiplicity of determinantal and Pfaffian ideals”, Adv. Math. 96:1 (1992), 1–37.
Hironaka [1975] H., Hironaka, “Triangulations of algebraic sets”, pp. 165–185 in Algebraic geometry (Arcata, CA, 1974), edited by R., Hartshorne, Proc. Sympos. Pure Math. 29, Amer. Math. Soc., Providence, RI, 1975.
Hirzebruch [1966] F., Hirzebruch, Topological methods in algebraic geometry, 3rd ed., Grundlehren der Mathematischen Wissenschaften 131, Springer, New York, 1966.
Hochster [1973] M., Hochster, “Grassmannians and their Schubert subvarieties are arithmetically Cohen– Macaulay”, J. Algebra 25 (1973), 40–57.
Hochster [1977] M., Hochster, “The Zariski–Lipman conjecture in the graded case”, J. Algebra 47:2 (1977), 411–424.
Hochster and Laksov [1987] M., Hochster and D., Laksov, “The linear syzygies of generic forms”, Comm. Algebra 15:1-2 (1987), 227–239.
Hodge [1943] W. V. D., Hodge, “Some enumerative results in the theory of forms”, Proc. Cambridge Philos. Soc. 39 (1943), 22–30.
Hodge and Pedoe [1952] W. V. D., Hodge and D., Pedoe, Methods of algebraic geometry, II, Cambridge University Press, 1952.
Hoyt [1971] W. L.|Hoyt, “On the moving lemma for rational equivalence”, J. Indian Math. Soc. (N.S.) 35 (1971), 47–66.
Hulek [1979] K., Hulek, “Stable rank-2 vector bundles on P2 with c1 odd”, Math. Ann. 242:3 (1979), 241–266.
Hulek [2012] K., Hulek, Elementare algebraische Geometrie, 2nd ed., Springer Spektrum, Wiesbaden, 2012.
Illusie [1972] L., Illusie, Complexe cotangent et déformations, II, Lecture Notes in Math. 283, Springer, Berlin-New York, 1972.
Kempf [1971] G., Kempf, “Schubert methods with an application to algebraic curves”, Publ. Math Centrum 6 (1971).
Kempf and Laksov [1974] G., Kempf and D., Laksov, “The determinantal formula of Schubert calculus”, Acta Math. 132 (1974), 153–162.
Kleiman [1974] S. L., Kleiman, “The transversality of a general translate”, Compositio Math. 28 (1974), 287–297.
Kleiman [1976] S. L., Kleiman, “r-special subschemes and an argument of Severi's”, Advances in Math. 22:1 (1976), 1–31.
Kleiman [1984] S. L., Kleiman, “About the conormal scheme”, pp. 161–197 in Complete intersections (Acireale, 1983), edited by S., Greco and R., Strano, Lecture Notes in Math. 1092, Springer, Berlin, 1984.
Kleiman [1986] S. L., Kleiman, “Tangency and duality”, pp. 163–225 in Proceedings of the 1984 Vancouver conference in algebraic geometry, edited by J., Carrell et al., CMS Conf. Proc. 6, Amer. Math. Soc., Providence, RI, 1986.
Kleiman and Laksov [1972] S. L., Kleiman and D., Laksov, “On the existence of special divisors”, Amer. J. Math. 94 (1972), 431–436.
Kleiman and Laksov [1974] S. L., Kleiman and D., Laksov, “Another proof of the existence of special divisors”, Acta Math. 132 (1974), 163–176.
Kleiman and Speiser [1991] S. L., Kleiman and R., Speiser, “Enumerative geometry of nonsingular plane cubics”, pp. 85–113 in Algebraic geometry (Sundance 1988), edited by B., Harbourne and R., Speiser, Contemp. Math. 116, Amer. Math. Soc., Providence, RI, 1991.
Laksov [1987] D., Laksov, “Completed quadrics and linear maps”, pp. 371–387 in Algebraic geometry (Bowdoin, ME, 1985), edited by S. J., Bloch, Proc. Sympos. Pure Math. 46, Amer. Math. Soc., Providence, RI, 1987.
Landsberg [2012] J. M., Landsberg, Tensors: geometry and applications, Graduate Studies in Mathematics 128, Amer. Math. Soc., Providence, RI, 2012.
Larsen [1973] M. E., Larsen, “On the topology of complex projective manifolds”, Invent. Math. 19 (1973), 251–260.
Lazarsfeld [1986] R., Lazarsfeld, “Brill–Noether–Petri without degenerations”, J. Differential Geom. 23:3 (1986), 299–307.
Lazarsfeld [1994] R., Lazarsfeld, “Lectures on Linear Series”, lecture notes, 1994. Available at http://arxiv.org/abs/alg-geom/9408011.
Lefschetz [1950] S., Lefschetz, L'analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1950.
Lipman [1965] J., Lipman, “Free derivation modules on algebraic varieties”, Amer. J. Math. 87 (1965), 874–898.
Lojasiewicz [1964] S., Lojasiewicz, “Triangulation of semi-analytic sets”, Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 449–474.
Manin [1986] Y. I., Manin, Cubic forms, 2nd ed., North-Holland Mathematical Library 4, North-Holland, Amsterdam, 1986.
Maruyama [1983] M., Maruyama, “Singularities of the curve of jumping lines of a vector bundle of rank 2 on P2”, pp. 370–411 in Algebraic geometry (Tokyo/Kyoto, 1982), edited by M., Raynaud and T., Shioda, Lecture Notes in Math. 1016, Springer, Berlin, 1983.
Mather [1971] J. N., Mather, “Stability of C∞ mappings, VI: The nice dimensions”, pp. 207–253 in Singularities—Symposium I (Univ. Liverpool, 1969/70), edited by C. T. C., Wall, Lecture Notes in Math. 192, Springer, Berlin, 1971.
Mather [1973] J. N., Mather, “Generic projections”, Ann. of Math. (2) 98 (1973), 226–245.
Matsumura [2014] S.-I., Matsumura, “Weak Lefschetz theorems and the topology of zero loci of ample vector bundles”, Comm. Anal. Geom. 22:4 (2014), 595–616.
McCrory and Shifrin [1984] C., McCrory and T., Shifrin, “Cusps of the projective Gauss map”, J. Differential Geom. 19:1 (1984), 257–276.
Milne [2008] J. S., Milne, “Abelian varieties (v2.00)”, notes, 2008. Available at http://jmilne.org/math/CourseNotes/AV.pdf.
Milnor [1963] J., Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press, 1963.
Milnor [1965] J., Milnor, Topology from the differentiable viewpoint, The University Press of Virginia, Charlottesville, VA, 1965.
Milnor [1997] J., Milnor, Topology from the differentiable viewpoint, Princeton University Press, 1997. Revised reprint of the 1965 original.
Morrison [1993] D. R., Morrison, “Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians”, J. Amer. Math. Soc. 6:1 (1993), 223–247.
Mumford [1962] D., Mumford, “Further pathologies in algebraic geometry”, Amer. J. Math. 84 (1962), 642–648.
Mumford [1966] D., Mumford, Lectures on curves on an algebraic surface, Annals of Mathematics Studies 59, Princeton University Press, 1966.
Mumford [1976] D., Mumford, Algebraic geometry, I: Complex projective varieties, Grundlehren der Mathematischen Wissenschaften 221, Springer, Berlin-New York, 1976.
Mumford [1983] D., Mumford, “Towards an enumerative geometry of the moduli space of curves”, pp. 271–328 in Arithmetic and geometry, II, edited by M., Artin and J., Tate, Progr. Math. 36, Birkhäuser, Boston, 1983.
Mumford [2008] D., Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Hindustan Book Agency, New Delhi, 2008. Corrected reprint of the 1974 edition.
Okonek [1987] C., Okonek, “Barth–Lefschetz theorems for singular spaces”, J. Reine Angew. Math. 374 (1987), 24–38.
Palais [1965] R. S., Palais (editor), Seminar on the Atiyah–Singer index theorem, Annals of Mathematics Studies 57, Princeton University Press, 1965.
Pardue [1996] K., Pardue, “Deformation classes of graded modules and maximal Betti numbers”, Illinois J. Math. 40:4 (1996), 564–585.
Peeva and Stillman [2005] I., Peeva and M., Stillman, “Connectedness of Hilbert schemes”, J. Algebraic Geom. 14:2 (2005), 193–211.
Perkinson [1996] D., Perkinson, “Principal parts of line bundles on toric varieties”, Compositio Math. 104:1 (1996), 27–39.
Peskine and Szpiro [1974] C., Peskine and L., Szpiro, “Liaison des variétés algébriques, I”, Invent. Math. 26 (1974), 271–302.
Piene and Schlessinger [1985] R., Piene and M., Schlessinger, “On the Hilbert scheme compactification of the space of twisted cubics”, Amer. J. Math. 107:4 (1985), 761–774.
Porteous [1971] I. R., Porteous, “Simple singularities of maps”, pp. 286–307 in Singularities—Symposium I (Univ. Liverpool, 1969/70), edited by C. T. C., Wall, Lecture Notes in Math. 192, Springer, Berlin, 1971.
Ran [2005a] Z., Ran, “Geometry on nodal curves”, Compos. Math. 141:5 (2005), 1191–1212.
Ran [2005b] Z., Ran, “A note on Hilbert schemes of nodal curves”, J. Algebra 292:2 (2005), 429–446.
Re [2012] R., Re, “Principal parts bundles on projective spaces and quiver representations”, Rend. Circ. Mat. Palermo (2) 61:2 (2012), 179–198.
Reeves [1995] A. A., Reeves, “The radius of the Hilbert scheme”, J. Algebraic Geom. 4:4 (1995), 639–657.
Reid [1988] M., Reid, Undergraduate algebraic geometry, London Mathematical Society Student Texts 12, Cambridge University Press, 1988.
Riedl and Yang [2014] E., Riedl and D., Yang, “Kontsevich spaces of rational curves on Fano hypersurfaces”, preprint, 2014. Available at http://arxiv.org/abs/1409.3802.
Roberts [1972a] J., Roberts, “Chow's moving lemma”, pp. 89–96 in Algebraic geometry (Fifth Nordic Summer School, Oslo, 1970), edited by F., Oort, Wolters-Noordhoff, Groningen, 1972. Appendix 2 to “Motives”, by Steven L., Kleiman, pp. 53–82 of the same reference.
Roberts [1972b] J., Roberts, “The variation of singular cycles in an algebraic family of morphisms”, Trans. Amer. Math. Soc. 168 (1972), 153–164.
Russell [2003] H., Russell, “Counting singular plane curves via Hilbert schemes”, Adv. Math. 179:1 (2003), 38–58.
Samuel [1956] P., Samuel, “Rational equivalence of arbitrary cycles”, Amer. J. Math. 78 (1956), 383–400.
Samuel [1971] P., Samuel, “Séminaire sur l'équivalence rationnelle”, pp. 1–17 in Séminaire sur l'équivalence rationnelle (Paris-Orsay, 1971), edited by M., Flexor and J.-J., Risler, Publ. Math. Orsay 425, Dép. Math. Fac. Sci., Univ. Paris, Orsay, 1971.
Schubert [1979] H., Schubert, Kalkül der abzählenden Geometrie, Springer, Berlin-New York, 1979. Reprint of the 1879 original.
Segre [1943] B., Segre, “The maximum number of lines lying on a quartic surface”, Quart. J. Math., Oxford Ser. 14 (1943), 86–96.
Serre [1955] J.-P., Serre, “Faisceaux algébriques cohérents”, Ann. of Math. (2) 61 (1955), 197–278.
Serre [1955/1956] J.-P., Serre, “Géométrie algébrique et géométrie analytique”, Ann. Inst. Fourier, Grenoble 6 (1955/1956), 1–42.
Serre [1979] J.-P., Serre, Local fields, Graduate Texts in Mathematics 67, Springer, New York-Berlin, 1979.
Serre [2000] J.-P., Serre, Local algebra, Springer, Berlin, 2000.
Seshadri [2007] C. S., Seshadri, Introduction to the theory of standard monomials, Texts and Readings in Mathematics 46, Hindustan Book Agency, New Delhi, 2007. Revised reprint of the 1985 original.
Severi [1933] F., Severi, “Über die grundlagen der algebraischen Geometrie”, Abh. Math. Sem. Univ. Hamburg 9:1 (1933), 335–364.
Shafarevich [1994] I. R., Shafarevich, Basic algebraic geometry, I, 2nd ed., Springer, Berlin, 1994.
Smith [2000] G. G., Smith, “Computing global extension modules”, J. Symbolic Comput. 29:4-5 (2000), 729–746.
Smith et al. [2000] K. E., Smith, L., Kahanpää, P., Kekäläinen, and W., Traves, An invitation to algebraic geometry, Springer, New York, 2000.
Srinivas [2010] V., Srinivas, “Algebraic cycles on singular varieties”, pp. 603–623 in Proceedings of the International Congress of Mathematicians, II, edited by R., Bhatia et al., Hindustan Book Agency, New Delhi, 2010.
Stacks Project [2015] T. Stacks, Project, “Stacks Project”, 2015. Available at http://stacks.math.columbia.edu.
Stanley [1999] R. P., Stanley, Enumerative combinatorics, II, Cambridge Studies in Advanced Mathematics 62, Cambridge University Press, 1999.
Steiner [1848] J., Steiner, “Elementare Lösung einer geometrischen Aufgabe, und über einige damit in Beziehung stehende Eigenschaften der Kegelschnitte”, J. Reine Angew. Math. 37 (1848), 161–192.
Teissier [1977] B., Teissier, “The hunting of invariants in the geometry of discriminants”, pp. 565–678 in Real and complex singularities (Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), edited by P., Holm, Sijthoff & Noordhoff, Alphen aan den Rijn, 1977.
Terracini [1911] A., Terracini, “Sulle Vk per cui la varietà degli Sh.h (C)-seganti ha dimensione minore dell'ordinario”, Rend. Circ. Mat. Palermo 31 (1911), 392–396.
Totaro [2013] B., Totaro, “On the integral Hodge and Tate conjectures over a number field”, Forum Math. Sigma 1 (2013), e4, 13 pp.
Totaro [2014] B., Totaro, “Chow groups, Chow cohomology, and linear varieties”, Forum Math. Sigma 2 (2014), e17, 25 pp.
Vakil [2006a] R., Vakil, “A geometric Littlewood–Richardson rule”, Ann. of Math. (2) 164:2 (2006), 371–421.
Vakil [2006b] R., Vakil, “Murphy's law in algebraic geometry: badly-behaved deformation spaces”, Invent. Math. 164:3 (2006), 569–590.
Vogel [1984] W., Vogel, Lectures on results on Bezout's theorem, Tata Institute of Fundamental Research Lectures on Mathematics and Physics 74, Springer, Berlin, 1984.
Voloch [2003] J. F., Voloch, “Surfaces in ℙ3 over finite fields”, pp. 219–226 in Topics in algebraic and noncommutative geometry (Luminy/Annapolis, MD, 2001), edited by C. G., Melles et al., Contemp. Math. 324, Amer. Math. Soc., Providence, RI, 2003.
Whitney [1941] H., Whitney, “On the topology of differentiable manifolds”, pp. 101–141 in Lectures in Topology, edited by R., Wilder and W., Ayres, University of Michigan Press, Ann Arbor, MI, 1941.
Zak [1991] F. L., Zak, “Some properties of dual varieties and their applications in projective geometry”, pp. 273–280 in Algebraic geometry (Chicago, IL, 1989), edited by S., Bloch et al., Lecture Notes in Math. 1479, Springer, Berlin, 1991.
Zariski [1982] O., Zariski, “Dimension-theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes”, Amer. J. Math. 104:1 (1982), 209–226.

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