References
Published online by Cambridge University Press: aN Invalid Date NaN
Translated by
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Algebraic Varieties: Minimal Models and Finite Generation , pp. 237 - 244Publisher: Cambridge University PressPrint publication year: 2024
References
Abramovich, Dan and Karu, Kalle. 2000. Weak semistable reduction in characteristic 0. Invent. Math., 139(2), 241–273.CrossRefGoogle Scholar
Abramovich, Dan, Karu, Kalle, Matsuki, Kenji, and Włodarczyk, Jarosław. 2002. Torification and factorization of birational maps. J. Amer. Math. Soc., 15(3), 531–572.CrossRefGoogle Scholar
Alexeev, Valery. 1994. Boundedness and K2 for log surfaces. Internat. J. Math., 5(6), 779–810.CrossRefGoogle Scholar
Angehrn, Urban and Siu, Yum-Tong. 1995. Effective freeness and point separation for adjoint bundles. Invent. Math., 122(2), 291–308.CrossRefGoogle Scholar
Arbarello, Enrico, Cornalba, Maurizio, Griffiths, Phillip A., and Harris, Joe. 1985. Geometry of algebraic curves. Vol. I. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267. Springer-Verlag, New York.CrossRefGoogle Scholar
Artin, Michael. 1962. Some numerical criteria for contractability of curves on algebraic surfaces. Amer. J. Math., 84, 485–496.CrossRefGoogle Scholar
Artin, Michael. 1966. On isolated rational singularities of surfaces. Amer. J. Math., 88, 129–136.CrossRefGoogle Scholar
Artin, Michael and Mumford, David. 1972. Some elementary examples of unirational varieties which are not rational. Proc. London Math. Soc. (3), 25, 75–95.CrossRefGoogle Scholar
Barth, Wolf P., Hulek, Klaus, Peters, Chris A. M., and Van de Ven, Antonius. 1984. Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Beauville, Arnaud. 1983. Complex algebraic surfaces. London Mathematical Society Lecture Note Series, vol. 68. Cambridge University Press, Cambridge. Translated from the French by Richard Barlow, Nicholas I. Shepherd-Barron, and Miles Reid.Google Scholar
Bierstone, Edward and Milman, Pierre D. 1997. Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Invent. Math., 128(2), 207–302.CrossRefGoogle Scholar
Birkar, Caucher. 2010. On existence of log minimal models. Compos. Math., 146(4), 919–928.CrossRefGoogle Scholar
Birkar, Caucher. 2019. Anti-pluricanonical systems on Fano varieties. Ann. Math. (2), 190(2), 345–463.CrossRefGoogle Scholar
Birkar, Caucher. 2021. Singularities of linear systems and boundedness of Fano varieties. Ann. Math. (2), 193(2), 347–405.CrossRefGoogle Scholar
Birkar, Caucher and Shokurov, Vyacheslav V. 2010. Mld’s vs thresholds and flips. J. Reine Angew. Math., 638, 209–234.Google Scholar
Birkar, Caucher, Cascini, Paolo, Hacon, Christopher D., and McKernan, James. 2010. Existence of minimal models for varieties of log general type. J. Amer. Math. Soc., 23(2), 405–468.CrossRefGoogle Scholar
Bombieri, Enrico. 1973. Canonical models of surfaces of general type. Inst. Hautes Études Sci. Publ. Math., 171–219.CrossRefGoogle Scholar
Bombieri, Enrico and Mumford, David. 1976. Enriques’ classification of surfaces in char. p. III. Invent. Math., 35, 197–232.CrossRefGoogle Scholar
Bombieri, Enrico and Mumford, David. 1977. Enriques’ classification of surfaces in char. p. II. In Baily, Walter L. Jr. and Shioda, Tetsuji (eds.), Complex analysis and algebraic geometry. Cambridge University Press, Cambridge, pp. 23–42.CrossRefGoogle Scholar
Borisov, Alexander A. and Borisov, Lev A. 1992. Singular toric Fano three-folds. Mat. Sb., 183(2), 134–141.Google Scholar
Campana, Frédéric and Peternell, Thomas. 2011. Geometric stability of the cotangent bundle and the universal cover of a projective manifold. Bull. Soc. Math. France, 139(1), 41–74. With an appendix by Matei Toma.CrossRefGoogle Scholar
Campana, Frédéric, Koziarz, Vincent, and Păun, Mihai. 2012. Numerical character of the effectivity of adjoint line bundles. Ann. Inst. Fourier (Grenoble), 62(1), 107–119.CrossRefGoogle Scholar
Clemens, C. Herbert and Griffiths, Phillip A. 1972. The intermediate Jacobian of the cubic threefold. Ann. Math. (2), 95, 281–356.CrossRefGoogle Scholar
Druel, Stéphane. 2011. Quelques remarques sur la décomposition de Zariski divisorielle sur les variétés dont la première classe de Chern est nulle. Math. Z., 267(1–2), 413–423.CrossRefGoogle Scholar
Francia, Paolo. 1980. Some remarks on minimal models. I. Compositio Math., 40(3), 301–313.Google Scholar
Fujiki, Akira. 1980. On the minimal models of complex manifolds. Math. Ann., 253(2), 111–128.CrossRefGoogle Scholar
Fujino, Osamu. 2007. Special termination and reduction to pl flips. In Corti, Alessio (ed.), Flips for 3-folds and 4-folds. Oxford Lecture Ser. Math. Appl., vol. 35. Oxford University Press, Oxford, pp. 63–75.CrossRefGoogle Scholar
Fujino, Osamu. 2011. On Kawamata’s theorem. In Faber, Carel, van der Geer, Gerard, and Looijenga, Eduard (eds.), Classification of algebraic varieties. EMS Ser. Congr. Rep. Eur. Math. Soc., Zürich, pp. 305–315.Google Scholar
Fujino, Osamu and Mori, Shigefumi. 2000. A canonical bundle formula. J. Differential Geom., 56(1), 167–188.CrossRefGoogle Scholar
Fujita, Takao. 1979. On Zariski problem. Proc. Japan Acad. Ser. A Math. Sci., 55(3), 106–110.CrossRefGoogle Scholar
Fulton, William. 1993. Introduction to toric varieties. Annals of Mathematics Studies, vol. 131. Roever Lectures in Geometry. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Gongyo, Yoshinori. 2011. On the minimal model theory for dlt pairs of numerical log Kodaira dimension zero. Math. Res. Lett., 18(5), 991–1000.CrossRefGoogle Scholar
Grauert, Hans. 1962. Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann., 146, 331–368.CrossRefGoogle Scholar
Grothendieck, Alexander. 1962. Fondements de la géométrie algébrique [Extraits du Séminaire Bourbaki, 1957–1962.] Secrétariat mathématique, Paris.Google Scholar
Hacon, Christopher D. and McKernan, James. 2006. Boundedness of pluricanonical maps of varieties of general type. Invent. Math., 166(1), 1–25.CrossRefGoogle Scholar
Hacon, Christopher D. and McKernan, James. 2007a. Extension theorems and the existence of flips. In Corti, Alessio (ed.), Flips for 3-folds and 4-folds. Oxford Lecture Ser. Math. Appl., vol. 35. Oxford University Press, Oxford, pp. 76–110.CrossRefGoogle Scholar
Hacon, Christopher D. and McKernan, James. 2007b. On Shokurov’s rational connectedness conjecture. Duke Math. J., 138(1), 119–136.CrossRefGoogle Scholar
Hacon, Christopher D. and McKernan, James. 2010. Existence of minimal models for varieties of log general type. II. J. Amer. Math. Soc., 23(2), 469–490.CrossRefGoogle Scholar
Hacon, Christopher D. and McKernan, James. 2013. The Sarkisov program. J. Algebraic Geom., 22(2), 389–405.CrossRefGoogle Scholar
Hacon, Christopher D. and Xu, Chenyang. 2013. Existence of log canonical closures. Invent. Math., 192(1), 161–195.CrossRefGoogle Scholar
Hacon, Christopher D. and Xu, Chenyang. 2015. On the three dimensional minimal model program in positive characteristic. J. Amer. Math. Soc., 28(3), 711–744.CrossRefGoogle Scholar
Hacon, Christopher D., McKernan, James, and Xu, Chenyang. 2013. On the birational automorphisms of varieties of general type. Ann. Math. (2), 177(3), 1077–1111.CrossRefGoogle Scholar
Hacon, Christopher D., McKernan, James, and Xu, Chenyang. 2014. ACC for log canonical thresholds. Ann. Math. (2), 180(2), 523–571.CrossRefGoogle Scholar
Hartshorne, Robin. 1977. Algebraic geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York.CrossRefGoogle Scholar
Hironaka, Heisuke. 1964. Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. Math. (2), 79, 109–203; (2), 79, 205–326.CrossRefGoogle Scholar
Hironaka, Heisuke. 1977. Idealistic exponents of singularity. In Igusa, Jun-Ichi (ed.), Algebraic geometry. (J. J. Sylvester Sympos., Johns Hopkins University, Baltimore, MD, 1976), pp. 52–125.Google Scholar
Iitaka, Shigeru. 1982. Algebraic geometry: An introduction to birational geometry of algebraic varieties. North-Holland Mathematical Library, vol. 24. Springer-Verlag, New York.CrossRefGoogle Scholar
Iskovskih, Vasily A. 1977. Fano threefolds. I. Izv. Akad. Nauk SSSR Ser. Mat., 41(3), 516–562, 717.Google Scholar
Iskovskih, Vasily A. 1978. Fano threefolds. II. Izv. Akad. Nauk SSSR Ser. Mat., 42(3), 506–549.Google Scholar
Iskovskih, Vasily A. and Manin, Yuri I. 1971. Three-dimensional quartics and counterexamples to the Lüroth problem. Mat. Sb. (N.S.), 86(128), 140–166.Google Scholar
Kawamata, Yujiro. 1979. On the classification of noncomplete algebraic surfaces. In Lønsted, Knud (ed.), Algebraic geometry (Proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978). Lecture Notes in Math., vol. 732. Springer, Berlin, pp. 215–232.CrossRefGoogle Scholar
Kawamata, Yujiro. 1981. Characterization of abelian varieties. Compositio Math., 43(2), 253–276.Google Scholar
Kawamata, Yujiro. 1982. A generalization of Kodaira-Ramanujam’s vanishing theorem. Math. Ann., 261(1), 43–46.CrossRefGoogle Scholar
Kawamata, Yujiro. 1984a. The cone of curves of algebraic varieties. Ann. Math. (2), 119(3), 603–633.CrossRefGoogle Scholar
Kawamata, Yujiro. 1984b. Elementary contractions of algebraic 3-folds. Ann. Math. (2), 119(1), 95–110.CrossRefGoogle Scholar
Kawamata, Yujiro. 1984c. On the finiteness of generators of a pluricanonical ring for a 3-fold of general type. Amer. J. Math., 106(6), 1503–1512.CrossRefGoogle Scholar
Kawamata, Yujiro 1985a. Pluricanonical systems on minimal algebraic varieties. Invent. Math., 79(3), 567–588.CrossRefGoogle Scholar
Kawamata, Yujiro. 1985b. Minimal models and the Kodaira dimension of algebraic fiber spaces. J. Reine Angew. Math., 363, 1–46.Google Scholar
Kawamata, Yujiro. 1986. On the plurigenera of minimal algebraic 3-folds with K ≡ 0. Math. Ann., 275(4), 539–546.CrossRefGoogle Scholar
Kawamata, Yujiro. 1987. The Zariski decomposition of log-canonical divisors. In Bloch , Spencer J.(ed.), Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985). Proc. Sympos. Pure Math., vol. 46. Amer. Math. Soc., Providence, RI, pp. 425–433.Google Scholar
Kawamata, Yujiro. 1988. Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces. Ann. Math. (2), 127(1), 93–163.CrossRefGoogle Scholar
Kawamata, Yujiro. 1989. Small contractions of four-dimensional algebraic manifolds. Math. Ann., 284(4), 595–600.CrossRefGoogle Scholar
Kawamata, Yujiro. 1992a. Abundance theorem for minimal threefolds. Invent. Math., 108(2), 229–246.CrossRefGoogle Scholar
Kawamata, Yujiro. 1992b. Boundedness of Q-Fano threefolds. In Bokut, Leonid A., Ershov, Yuri L., and Kostrikin, Alexei I. (eds.), Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989). Contemp. Math., vol. 131. Amer. Math. Soc., Providence, RI, pp. 439–445.Google Scholar
Kawamata, Yujiro. 1992c. Termination of log flips for algebraic 3-folds. Internat. J. Math., 3(5), 653–659.CrossRefGoogle Scholar
Kawamata, Yujiro. 1994. Semistable minimal models of threefolds in positive or mixed characteristic. J. Algebraic Geom., 3(3), 463–491.Google Scholar
Kawamata, Yujiro. 1997b. On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann., 308(3), 491–505.CrossRefGoogle Scholar
Kawamata, Yujiro. 1998. Subadjunction of log canonical divisors. II. Amer. J. Math., 120(5), 893–899.CrossRefGoogle Scholar
Kawamata, Yujiro. 1999a. Deformations of canonical singularities. J. Amer. Math. Soc., 12(1), 85–92.CrossRefGoogle Scholar
Kawamata, Yujiro. 1999b. On the extension problem of pluricanonical forms. In Pragacz, Piotr, Szurek, Michał, and Wiśniewski, Jaroslaw (eds.), Algebraic geometry: Hirzebruch 70 (Warsaw, 1998). Contemp. Math., vol. 241. Amer. Math. Soc., Providence, RI, pp. 193–207.CrossRefGoogle Scholar
Kawamata, Yujiro. 2008. Flops connect minimal models. Publ. Res. Inst. Math. Sci., 44(2), 419–423.CrossRefGoogle Scholar
Kawamata, Yujiro. 2011. Remarks on the cone of divisors. In Faber, Carel, van der Geer, Gerard, and Looijenga, Eduard (eds.), Classification of algebraic varieties. EMS Ser. Congr. Rep. Eur. Math. Soc., Zürich, pp. 317–325.Google Scholar
Kawamata, Yujiro. 2013. On the abundance theorem in the case of numerical Kodaira dimension zero. Amer. J. Math., 135(1), 115–124.CrossRefGoogle Scholar
Kawamata, Yujiro. 2015. Variation of mixed Hodge structures and the positivity for algebraic fiber spaces. In Chen, Jungkai Alfred, Chen, Meng, Kawamata, Yujiro, and Keum, JongHae (eds.), Algebraic geometry in east Asia – Taipei 2011. Adv. Stud. Pure Math., vol. 65. Math. Soc. Japan, Tokyo, pp. 27–57.CrossRefGoogle Scholar
Kawamata, Yujiro, Matsuda, Katsumi, and Matsuki, Kenji 1987. Introduction to the minimal model problem. In Oda, Tadao (ed.), Algebraic geometry, Sendai, 1985. Adv. Stud. Pure Math., vol. 10. North-Holland, Amsterdam, pp. 283–360.CrossRefGoogle Scholar
Keel, Seán 1999. Basepoint freeness for nef and big line bundles in positive characteristic. Ann. Math. (2), 149(1), 253–286.CrossRefGoogle Scholar
Keel, Sean, Matsuki, Kenji, and McKernan, James. 1994. Log abundance theorem for threefolds. Duke Math. J., 75(1), 99–119.CrossRefGoogle Scholar
Kempf, George, Knudsen, Finn F., Mumford, David, and Saint-Donat, Bernard. 1973. Toroidal embeddings. I. Lecture Notes in Mathematics, vol. 339. Springer-Verlag, Berlin-New York.CrossRefGoogle Scholar
Kleiman, Steven L. 1966. Toward a numerical theory of ampleness. Ann. Math. (2), 84, 293–344.CrossRefGoogle Scholar
Klemm, Albrecht and Schimmrigk, Rolf. 1994. Landau-Ginzburg string vacua. Nuclear Phys. B, 411(2–3), 559–583.CrossRefGoogle Scholar
Kodaira, Kunihiko. 1953. On a differential-geometric method in the theory of analytic stacks. Proc. Nat. Acad. Sci. USA, 39, 1268–1273.CrossRefGoogle ScholarPubMed
Kodaira, Kunihiko. 1954. On Kähler varieties of restricted type (an intrinsic characterization of algebraic varieties). Ann. Math. (2), 60, 28–48.CrossRefGoogle Scholar
Kollár, János. 1993. Effective base point freeness. Math. Ann., 296(4), 595–605.CrossRefGoogle Scholar
Kollár, János. 1996. Rational curves on algebraic varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kollár, János and Mori, Shigefumi. 1998. Birational geometry of algebraic varieties. Cambridge Tracts in Mathematics, vol. 134. Cambridge University Press, Cambridge. With the collaboration of C. Herbert Clemens and Alessio Corti. Translated from the 1998 Japanese original.CrossRefGoogle Scholar
Kollár, János, Miyaoka, Yoichi, and Mori, Shigefumi. 1992a. Rational connectedness and boundedness of Fano manifolds. J. Differential Geom., 36(3), 765–779.CrossRefGoogle Scholar
Kollár, János, Miyaoka, Yoichi, and Mori, Shigefumi. 1992b. Rational curves on Fano varieties. In Ballico, Edoardo, Cantanese, Fabrizio, and Ciliberto, Ciro (eds.), Classification of irregular varieties (Trento, 1990). Lecture Notes in Math., vol. 1515. Springer, Berlin, pp. 100–105.CrossRefGoogle Scholar
Kollár, János, Miyaoka, Yoichi, and Mori, Shigefumi. 1992c. Rationally connected varieties. J. Algebraic Geom., 1(3), 429–448.Google Scholar
Kollár, János, Miyaoka, Yoichi, Mori, Shigefumi, and Takagi, Hiromichi. 2000. Boundedness of canonical Q-Fano 3-folds. Proc. Japan Acad. Ser. A Math. Sci., 76(5), 73–77.CrossRefGoogle Scholar
Kollár, János 1992. Flips and abundance for algebraic threefolds. Société Mathématique de France, Paris. Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Salt Lake City, Utah, August 1991, Astérisque No. 211 (1992) (1992).Google Scholar
Lazarsfeld, Robert. 2004. Positivity in algebraic geometry. I. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48. Springer-Verlag, Berlin. Classical setting: line bundles and linear series.Google Scholar
Lesieutre, John. 2016. A pathology of asymptotic multiplicity in the relative setting. Math. Res. Lett., 23(5), 1433–1451.CrossRefGoogle Scholar
Miyaoka, Yoichi. 1987. The Chern classes and Kodaira dimension of a minimal variety. In Oda, Tadao (ed.), Algebraic geometry, Sendai, 1985. Adv. Stud. Pure Math., vol. 10. North-Holland, Amsterdam, pp. 449–476.CrossRefGoogle Scholar
Miyaoka, Yoichi. 1988a. Abundance conjecture for 3-folds: case ν = 1. Compositio Math., 68(2), 203–220.Google Scholar
Miyaoka, Yoichi. 1988b. On the Kodaira dimension of minimal threefolds. Math. Ann., 281(2), 325–332.CrossRefGoogle Scholar
Miyaoka, Yoichi and Mori, Shigefumi. 1986. A numerical criterion for uniruledness. Ann. Math. (2), 124(1), 65–69.CrossRefGoogle Scholar
Mori, Shigefumi. 1979. Projective manifolds with ample tangent bundles. Ann. Math. (2), 110(3), 593–606.CrossRefGoogle Scholar
Mori, Shigefumi. 1982. Threefolds whose canonical bundles are not numerically effective. Ann. Math. (2), 116(1), 133–176.CrossRefGoogle Scholar
Mori, Shigefumi. 1985. On 3-dimensional terminal singularities. Nagoya Math. J., 98, 43–66.CrossRefGoogle Scholar
Mori, Shigefumi. 1988. Flip theorem and the existence of minimal models for 3-folds. J. Amer. Math. Soc., 1(1), 117–253.CrossRefGoogle Scholar
Mori, Shigefumi and Mukai, Shigeru. 2004. Extremal rays and Fano 3-folds. In Collino, Alberto, Conte, Alberto, and Fano, Gino (eds.), The fano conference. University of Torino, Turin, pp. 37–50.Google Scholar
Mukai, Shigeru. 1995. New developments in Fano manifold theory related to the vector bundle method and moduli problems. Sūgaku, 47(2), 125–144.Google Scholar
Mumford, David. 1961a. Pathologies of modular algebraic surfaces. Amer. J. Math., 83, 339–342.CrossRefGoogle Scholar
Mumford, David. 1961b. The topology of normal singularities of an algebraic surface and a criterion for simplicity. Inst. Hautes Études Sci. Publ. Math., 9, 5–22.CrossRefGoogle Scholar
Mumford, David. 1962. Further pathologies in algebraic geometry. Amer. J. Math., 84, 642–648.CrossRefGoogle Scholar
Mumford, David. 1969. Enriques’ classification of surfaces in char p. I. In Global analysis (Papers in Honor of K. Kodaira). University of Tokyo Press, Tokyo, pp. 325–339.Google Scholar
Nadel, Alan M. 1990. Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature. Ann. Math. (2), 132(3), 549–596.CrossRefGoogle Scholar
Nakano, Shigeo. 1973. Vanishing theorems for weakly 1-complete manifolds. In Kusunoki, Yusuke, Mizohata, Sigeru, Nagata, Masayoshi, Toda, Hiroshi, Yamaguti, Masaya, and Yoshizawa, Hiroki (eds.), Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki. Kinokuniya Book Store Co. Ltd., Tokyo, pp. 169–179.Google Scholar
Nakano, , , Shigeo. 1974/75. Vanishing theorems for weakly 1-complete manifolds. II. Publ. Res. Inst. Math. Sci., 10(1), 101–110.CrossRefGoogle Scholar
Nakayama, Noboru. 1986. Invariance of the plurigenera of algebraic varieties under minimal model conjectures. Topology, 25(2), 237–251.CrossRefGoogle Scholar
Nakayama, Noboru. 1987. The lower semicontinuity of the plurigenera of complex varieties. In Oda, Tadao (ed.), Algebraic geometry, Sendai, 1985. Adv. Stud. Pure Math., vol. 10. North-Holland, Amsterdam, pp. 551–590.CrossRefGoogle Scholar
Nakayama, Noboru. 2004. Zariski-decomposition and abundance. MSJ Memoirs, vol. 14. Mathematical Society of Japan, Tokyo.Google ScholarPubMed
Norimatsu, Yoshiki. 1978. Kodaira vanishing theorem and Chern classes for ∂-manifolds. Proc. Japan Acad. Ser. A Math. Sci., 54(4), 107–108.CrossRefGoogle Scholar
Raynaud, M. 1978. Contre-exemple au “vanishing theorem” en caractéristique p > 0. In Ramanathan, Kollagunta G. (ed.), C. P. Ramanujam – a tribute. Tata Inst. Fund. Res. Studies in Math., vol. 8. Springer, Berlin-New York, pp. 273–278.Google Scholar
Reid, Miles Projective morphisms according to Kawamata. Warwick preprint, 1983 (unpublished), www.maths.warwick.ac.uk/~miles/3folds/Ka.pdfGoogle Scholar
Reid, Miles. 1983a. Decomposition of toric morphisms. In Artin, Michael and Tate, John (eds.), Arithmetic and geometry, Vol. II. Progr. Math., vol. 36. Birkhäuser Boston, Boston, MA, pp. 395–418.CrossRefGoogle Scholar
Reid, Miles. 1983b. Minimal models of canonical 3-folds. In Iitaka, Shigeru (ed.), Algebraic varieties and analytic varieties (Tokyo, 1981). Adv. Stud. Pure Math., vol. 1. North-Holland, Amsterdam, pp. 131–180.CrossRefGoogle Scholar
Reid, Miles. 1987a. The moduli space of 3-folds with K = 0 may nevertheless be irreducible. Math. Ann., 278(1–4), 329–334.CrossRefGoogle Scholar
Reid, Miles. 1987b. Young person’s guide to canonical singularities. In Bloch, Spencer J. (ed.), Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985). Proc. Sympos. Pure Math., vol. 46. Amer. Math. Soc., Providence, RI, pp. 345–414.Google Scholar
Sakai, Fumio. 1982. Anti-Kodaira dimension of ruled surfaces. Sci. Rep. Saitama Univ. Ser. A, 10(2), 1–7.Google Scholar
Serre, Jean-Pierre. 1955. Faisceaux algébriques cohérents. Ann. Math. (2), 61, 197–278.CrossRefGoogle Scholar
Shokurov, Vyacheslav V. 1985. A nonvanishing theorem. Izv. Akad. Nauk SSSR Ser. Mat., 49(3), 635–651.Google Scholar
Shokurov, Vyacheslav V. 1992. Three-dimensional log perestroikas. Izv. Ross. Akad. Nauk Ser. Mat., 56(1), 105–203.Google Scholar
Shokurov, Vyacheslav V. 1996. 3-fold log models. Algebraic geometry, 4. J. Math. Sci., 81(3), 2667–2699.CrossRefGoogle Scholar
Shokurov, Vyacheslav V. 2003. Prelimiting flips. Tr. Mat. Inst. Steklova, 240(Biratsion. Geom. Lineĭn. Sist. Konechno Porozhdennye Algebry), 82–219.Google Scholar
Shokurov, Vyacheslav V. 2004. Letters of a bi-rationalist. V. Minimal log discrepancies and termination of log flips. Tr. Mat. Inst. Steklova, 246(Algebr. Geom. Metody, Svyazi i Prilozh.), 328–351.Google Scholar
Shokurov, Vyacheslav and Choi, Sung Rak. 2011. Geography of log models: theory and applications. Cent. Eur. J. Math., 9(3), 489–534.CrossRefGoogle Scholar
Siu, Yum-Tong. 1998. Invariance of plurigenera. Invent. Math., 134(3), 661–673.CrossRefGoogle Scholar
Siu, Yum-Tong. 2002. Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type. In Bauer, Ingrid, Catanese, Fabrizio, Kawamata, Yujiro, Peternell, Thomas, and Siu, Yum-Tong (eds.), Complex geometry (Göttingen, 2000). Springer, Berlin, pp. 223–277.CrossRefGoogle Scholar
Siu, Yum-Tong. 2011. Abundance conjecture. In Ji, Lizhen (ed.), Geometry and analysis. No. 2. Adv. Lect. Math. (ALM), vol. 18. Int. Press, Somerville, MA, pp. 271–317.Google Scholar
Szabó, Endre. 1994. Divisorial log terminal singularities. J. Math. Sci. Univ. Tokyo, 1(3), 631–639.Google Scholar
Takayama, Shigeharu. 2006. Pluricanonical systems on algebraic varieties of general type. Invent. Math., 165(3), 551–587.CrossRefGoogle Scholar
Tsuji, Hajime. 1992. Analytic Zariski decomposition. Proc. Japan Acad. Ser. A Math. Sci., 68(7), 161–163.CrossRefGoogle Scholar
Villamayor, Orlando. 1989. Constructiveness of Hironaka’s resolution. Ann. Sci. École Norm. Sup. (4), 22(1), 1–32.CrossRefGoogle Scholar
Włodarczyk, Jarosław. 2003. Toroidal varieties and the weak factorization theorem. Invent. Math., 154(2), 223–331.CrossRefGoogle Scholar
Włodarczyk, Jarosław. 2005. Simple Hironaka resolution in characteristic zero. J. Amer. Math. Soc., 18(4), 779–822.CrossRefGoogle Scholar
Włodarczyk, Jarosław. 2009. Simple constructive weak factorization. In Abramovich, Dan, Bertram, Aaron, Katzarkov, Ludmil, Pandharipande, Rahul, and Thaddeus, Michael (eds.), Algebraic geometry – Seattle 2005. Part 2. Proc. Sympos. Pure Math., vol. 80. Amer. Math. Soc., Providence, RI, pp. 957–1004.Google Scholar
Zariski, Oscar. 1962. The theorem of Riemann–Roch for high multiples of an effective divisor on an algebraic surface. Ann. Math. (2), 76, 560–615.CrossRefGoogle Scholar