Agarwal, P. K., Apfelbaum, R., Purdy, G. and Sharir, M. (2007) Similar simplices in a d-dimensional point set. In Proc. 23rd ACM Symposium on Computational Geometry, pp. 232–238.
Agarwal, P. K., Matoušek, J. and Sharir, M. (2013) On range searching with semialgebraic sets~II. SIAM J. Comput. 42 2039–2062.
Agarwal, P., Nevo, E., Pach, J., Pinchasi, R., Sharir, M. and Smorodinsky, S. (2004) Lenses in arrangements of pseudocircles and their applications. J. Assoc. Comput. Mach. 51 139–186.
Akutsu, T., Tamaki, H. and Tokuyama, T. (1998) Distribution of distances and triangles in a point set and algorithms for computing the largest common point sets. Discrete Comput. Geom. 20 307–331.
Alon, N. (1995) Tools from higher algebra. In Handbook of Combinatorics, Vols~1, 2, Elsevier, pp. 1749–1783.
Apfelbaum, R. and Sharir, M. (2011) Non-degenerate spheres in three dimensions. Combin. Probab. Comput. 20 503–512.
Aronov, B., Koltun, V. and Sharir, M. (2005) Incidences between points and circles in three and higher dimensions, Discrete Comput. Geom. 33 185–206.
Aronov, B. and Sharir, M. (2002) Cutting circles into pseudo-segments and improved bounds for incidences. Discrete Comput. Geom. 28 475–490.
Basu, S. and Sombra, M. Polynomial partitioning on varieties and point–hypersurface incidences in four dimensions. arXiv:1406.2144.
Beauville, A. (1996) Complex Algebraic Surfaces, second edition, Vol. 34 of London Mathematical Society Student Texts, Cambridge University Press.
Bochnak, J., Coste, M. and Roy, M. (1998) Real Algebraic Geometry, Springer.
Brass, P. (2002) Combinatorial geometry problems in pattern recognition. Discrete Comput. Geom. 28 495–510.
Chazelle, B., Edelsbrunner, H., Guibas, L. J., Sharir, M. and Stolfi, J. (1996) Lines in space: Combinatorics and algorithms. Algorithmica 15 428–447.
Cox, D., Little, J. and O'Shea, D. (2004) Using Algebraic Geometry, second edition, Springer.
Cox, D., Little, J. and O'Shea, D. (2007) Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, third edition, Springer.
Elekes, G., Kaplan, H. and Sharir, M. (2011) On lines, joints, and incidences in three dimensions. J. Combin. Theory Ser. A 118 962–977.
Elekes, G. and Sharir, M. (2011) Incidences in three dimensions and distinct distances in the plane. Combin. Probab. Comput. 20 571–608.
Erdős, P. (1946) On sets of distances of n points. Amer. Math. Monthly 53 248–250.
Fox, J., Pach, J., Sheffer, A., Suk, A. and Zahl, J. A semi-algebraic version of Zarankiewicz's problem, arXiv:1407.5705.
Fuchs, D. and Tabachnikov, S. (2007) Mathematical Omnibus: Thirty Lectures on Classical Mathematics, AMS.
Fulton, W. (1998) Intersection Theory, Springer.
Guth, L. Distinct distance estimates and low degree polynomial partitioning. arXiv:1404.2321.
Guth, L. and Katz, N. H. (2010) Algebraic methods in discrete analogs of the Kakeya problem. Adv. Math. 225 2828–2839.
Guth, L. and Katz, N. H. On the Erdős distinct distances problem in the plane. Ann. of Math., to appear. arXiv:1011.4105.
Harris, J. (1992) Algebraic Geometry: A First Course, Springer.
Hartshorne, R. (1983) Algebraic Geometry, Springer.
Hartshorne, R. (2000) Geometry: Euclid and Beyond, Springer.
Hwang, J. M. (2005) A bound on the number of curves of a given degree through a general point of a projective variety. Compositio Math. 141 703–712.
Kaplan, H., Matoušek, J., Safernová, Z. and Sharir, M. (2012) Unit distances in three dimensions. Combin. Probab. Comput. 21 597–610.
Kaplan, H., Matoušek, J. and Sharir, M. (2012) Simple proofs of classical theorems in discrete geometry via the Guth–Katz polynomial partitioning technique. Discrete Comput. Geom. 48 499–517.
Kaplan, H., Sharir, M. and Shustin, E. (2010) On lines and joints. Discrete Comput. Geom. 44 838–843.
Landsberg, J. M. (1999) Is a linear space contained in a submanifold? On the number of derivatives needed to tell. J. Reine Angew. Math. 508 53–60.
Landsberg, J. M. (2003) Lines on projective varieties. J. Reine Angew. Math. 562 1–3.
Marcus, A. and Tardos, G. (2006) Intersection reverse sequences and geometric applications. J. Combin. Theory Ser. A 113 675–691.
Matoušek, J. (2002) Lectures on Discrete Geometry, Springer.
Milnor, J. (1964) On the Betti numbers of real varieties. Proc. Amer. Math. Soc. 15 275–280.
Miranda, R. (1995) Algebraic Curves and Riemann Surfaces, Vol. 5 of Graduate Studies in Mathematics, AMS.
Nilov, F. and Skopenkov, M. (2013) A surface containing a line and a circle through each point is a quadric. Geom. Dedicata 163 301–310.
Pach, J. and Sharir, M. (2004) Geometric incidences. In Towards a Theory of Geometric Graphs (Pach, J., ed.), Vol. 342 of Contemporary Mathematics, AMS, pp. 185–223.
Quilodrán, R. (2010) The joints problem in Rn. SIAM J. Discrete Math. 23 2211–2213.
Roy, M.-F. and Vorobjov, N. (2002) The complexification and degree of a semi-algebraic set. Math. Z. 239 131–142.
Salmon, G. (1915) A Treatise on the Analytic Geometry of Three Dimensions, Vol. 2, fifth edition, Hodges, Figgis and Co. Ltd., Dublin.
Sard, A. (1942) The measure of the critical values of differentiable maps. Bull. Amer. Math. Soc. 48 883–890.
Sharir, M. and Solomon, N. (2014) Incidences between points and lines in four dimensions. In Proc. 30th ACM Symposium on Computational Geometry, 189–197.
Solymosi, J. and Tao, T. (2012) An incidence theorem in higher dimensions. Discrete Comput. Geom. 48 255–280.
Székely, L. (1997) Crossing numbers and hard Erdős problems in discrete geometry. Combin. Probab. Comput. 6 353–358.
Thom, R. (1965) Sur l'homologie des variétés algebriques réelles. In Differential and Combinatorial Topology (Cairns, S. S., ed.), Princeton University Press, pp. 255–265.
Warren, H. E. (1968) Lower bound for approximation by nonlinear manifolds. Trans. Amer. Math. Soc. 133 167–178.
Whitney, H. (1957) Elementary structure of real algebraic varieties. Ann. of Math. 66 545–556.
Zahl, J. (2013) An improved bound on the number of point–surface incidences in three dimensions. Contrib. Discrete Math. 8 100–121.
Zahl, J. A Szemerédi–Trotter type theorem in ℝ4. arXiv:1203.4600.