Quantum cohomology rings of toric manifolds
Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque no. 218  (1993), p. 9-34
     author = {Batyrev, Victor V.},
     title = {Quantum cohomology rings of toric manifolds},
     booktitle = {Journ\'ees de g\'eom\'etrie alg\'ebrique d'Orsay - Juillet 1992},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {218},
     year = {1993},
     pages = {9-34},
     language = {en},
     url = {http://www.numdam.org/item/AST_1993__218__9_0}
Batyrev, Victor V. Quantum cohomology rings of toric manifolds, in Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque, no. 218 (1993), pp. 9-34. http://www.numdam.org/item/AST_1993__218__9_0/

[1] P. S. Aspinwall and C. A. Lütken, and G. G. Ross, Construction and couplings of mirror manifolds, Phys. Lett. B 241, n.3, (1990), 373-380.

[2] P. S. Aspinwall and C. A. Lütken, Quantum algebraic geometry of superstring compactifications, Nuclear Physics B, 355 (1991), 482-510.

[3] P. S. Aspinwall, B. R. Greene, and D. R. Morrison, Multiple Mirror Manifolds and Topology Change in String Theory, Preprint IASSNS-HEP-93/4.

[4] M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress on Math., Birkhäuser-Verlag - Basel-Berlin, v. 93, 1991.

[5] V. V. Batyrev, On the classification of smooth projective toric varieties, Tôhoku Math. J. 43 (1991), 569-585.

[6] V. V. Batyrev, Dual polyhedra and the mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, to appear in Journal of Algebraic Geometry.

[7] V. V. Batyrev, Variations of the Mixed Hodge structure of Affine Hypersurfaces in Algebraic Tori, Duke Math. J, 69, (1993), 349-409.

[8] D. A. Cox, The Homogeneous Coordinate Ring of a Toric Variety, Preprint (1992).

[9] V. I. Danilov, The geometry of toric varieities, Russian Math. Survey, 33, n.2, (1978), 97-154.

[10] M. M. Kapranov, B. Sturmfels, and A. V. Zelevinsky, Chow polytopes and general resultants, Duke Math. J., 67 (1992) 189-218.

[11] T. Oda, Convex Bodies and Algebraic Geometry - An Introduction to the Theory of Toric Varieties, Ergebnisse der Math. (3) 15, Springer-Verlag, Berlin, Heildelberg, New York, London, Paris, Tokyo, 1988.

[12] T. Oda, H. S. Park, Linear Gale transform and Gelfand-Kapranov-Zelevinsky decompositions, Tôhoku Math. J. 43 (1991), 375-399.

[13] M. Reid, Decomposition of toric morphisms, in Arithmetic and Geometry, pepers dedicated to I.R. Shafarevich on the occasion of his 60th birfday (M. Artin and J. Tate, eds.), vol.II, Geometry, Progress in Math. 36, Birkhauser, Boston, Basel, Stuttgart, 1983, 395-418.

[14] B. Sturmfels, Gröbner bases of toric varieties, Tôhoku Math. J., 43, (1991), 249-261.

[15] C. Vafa, Topological Mirrors and Quantum Rings, in Essays on Mirror Manifolds, S.-T. Yau ed. (1992) 96-119.

[16] E. Witten, Two-dimensional gravity and intersection theory on moduli space, Survey in Diff. Geom. 1 (1991) 243-310.