@incollection{SB_1994-1995__37__275_0, author = {Kontsevich, Maxim}, title = {Mirror symmetry in dimension 3}, booktitle = {S\'eminaire Bourbaki : volume 1994/95, expos\'es 790-804}, series = {Ast\'erisque}, note = {talk:801}, pages = {275--293}, publisher = {Soci\'et\'e math\'ematique de France}, number = {237}, year = {1996}, mrnumber = {1423628}, zbl = {0880.14019}, language = {en}, url = {http://archive.numdam.org/item/SB_1994-1995__37__275_0/} }
TY - CHAP AU - Kontsevich, Maxim TI - Mirror symmetry in dimension 3 BT - Séminaire Bourbaki : volume 1994/95, exposés 790-804 AU - Collectif T3 - Astérisque N1 - talk:801 PY - 1996 SP - 275 EP - 293 IS - 237 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_1994-1995__37__275_0/ LA - en ID - SB_1994-1995__37__275_0 ER -
%0 Book Section %A Kontsevich, Maxim %T Mirror symmetry in dimension 3 %B Séminaire Bourbaki : volume 1994/95, exposés 790-804 %A Collectif %S Astérisque %Z talk:801 %D 1996 %P 275-293 %N 237 %I Société mathématique de France %U http://archive.numdam.org/item/SB_1994-1995__37__275_0/ %G en %F SB_1994-1995__37__275_0
Kontsevich, Maxim. Mirror symmetry in dimension 3, in Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Talk no. 801, 19 p. http://archive.numdam.org/item/SB_1994-1995__37__275_0/
[1] The monomial-divisor mirror map, Int. Math. Res. Notices (1993), 319-337, alg-geom/9309007. | DOI | MR | Zbl
, and ,[2] Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys. B416 (1994), 414-480, hep-th/9309097. | DOI | MR | Zbl
, and ,[3] Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262. | DOI | MR | Zbl
and ,[4] Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, Jour. Alg. Geom. 3 (1994), 493-535, alg-geom/9310003. | MR | Zbl
,[5] Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, alg-geom/9402002. | Zbl
and ,[6] Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toris varieties, alg-geom/ 9307010. | Zbl
and ,[7] Variétés kählériennes dont la première classe de Chern est nulle, Jour. Diff. Geom. 18 (1983), 755-782. | DOI | MR | Zbl
,[8] Holomorphic anomalies in topological field theories, with an appendix by , Nucl. Phys. B405 (1993), 298-304. | DOI | MR | Zbl
, , and ,[9] Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Comm. Math. Phys. 165 (1994), 311-427. | DOI | MR | Zbl
, , and ,[10] Singularités quotients non abéliennes de dimension 3 et variétés de Bogomolov, Prépublication de l'Institut Fourier 216 (1992). | Zbl
and ,[11] Hamiltonian Kähler manifolds, Dokl. Akad. Nauk SSSR 245 (1978), 1101-1104. | MR | Zbl
,[12] On the decomposition of Kähler manifolds with trivial canonical class, Math. USSR Sbornik 22 (1974), 580-583. | DOI | MR | Zbl
,[13] The space of Kähler metrics, in Proceedings of the International Congress of Mathematicians (Amsterdam 1954), Vol. 2, pp. 206-207. | Zbl
,[14] Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B 407 (1993), 115-154. | DOI | MR | Zbl
, and ,[15] Complete intersection Calabi-Yau manifolds. II. Three generation manifolds, Nucl. Phys. B306 (1988), 113-136. | DOI | MR
, and ,[16] Mirror symmetry for two-parameter models (I), Nucl. Phys. B416 (1994), 481-562, hep-th/9308083. | DOI | MR | Zbl
, , , and ,[17] A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B359 (1991), 21-74, and also in [60], pp. 31-95. | DOI | MR | Zbl
, , and ,[18] Mirror symmetry for two-parameter models - II, Nucl. Phys. B429 (1994), 624-674, hep-th/9403187. | DOI | MR | Zbl
, , and ,[19] Double solids, Adv. Math. 47 (1983), 107-230. | DOI | MR | Zbl
,[20] Some world-sheet properties of superstring compactifications, on orbifolds and otherwise, Superstrings, Unified Theories and Cosmology 1987 (G. Furlan et al. eds.), World Scientific, Singapore, 1988, pp. 67-126. | MR
,[21] The number of twisted cubic curves on the general quintic threefold, Math. Scan., to appear. | EuDML | MR | Zbl
and ,[22] On threefolds with trivial canonical bundle, Complex Geometry and Lie Theory (Proc. Symp. Pure Math., vol. 53), American Mathematical Society, Providence, 1991, pp. 103-134. | DOI | MR | Zbl
,[23] Conformal field theory, Séminaire Bourbaki 1988/89, n° 704, in Astérisque 177-178, pp. 95-126. | EuDML | Numdam | MR | Zbl
,[24] Mirror symmetry in higher dimension, hep-th/9402119.
, and ,[25] Duality in Calabi-Yau moduli space, Nucl. Phys. B338 (1990), 15-37. | DOI | MR
and ,[26] Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988), 431-441. | DOI | MR | Zbl
and ,[27] All the Hodge numbers for all Calabi-Yau complete intersections, Class. Quantum Grav. 6 (1989), 105-124. | DOI | MR | Zbl
, and ,[28] Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. | DOI | EuDML | MR | Zbl
,[29] Some examples of threefolds with trivial canonical bundle, Gesammelte Abhandlungen, Bd. II, Springer-Verlag, 1987, pp. 757-770. | MR
,[30] Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Comm. Math. Phys. 167 (1995), 301-350, hep-th/9308122. | DOI | MR | Zbl
, , and ,[31] Mirror symmetry, mirror map and applications to complete intersections Calabi-Yau spaces, Nucl. Phys. B433 (1995), 501-544, hep-th/9406055. | DOI | MR | Zbl
, , and ,[32] Mirror Symmetry and An Exact Calculation of Point Correlation Function on Calabi-Yau Manifold embedded in , hep-th/9409029. | DOI | Zbl
and ,[33] Rational curves on Calabi-Yau manifolds: verifying predictions of mirror symmetry, Projective Geometry with Applications (E. Ballico, ed.), Marcel Dekker, 1994, pp. 231-239, alg-geom/9301006. | MR | Zbl
,[34] Enumeration of rational curves via toric actions, MPI preprint 94-39, 1994, hep-th/9405035. | Zbl
,[35] Chiral rings in N = 2 superconformal theories, Nucl. Phys. B324 (1984), 427-474. | DOI | MR
, and ,[36] Mirror Maps, Modular Relations and Hypergeometric Series I, hep-th/9507151.
and ,[37] Lines on Calabi-Yau complete intersections, mirror symmetry and Picard-Fuchs equations, Intern. Math. Res. Not. 1 (1993), 29-39. | DOI | MR | Zbl
and ,[38] Generating functions in algebraic geometry and sums over trees, MPI preprint, 1994, alg-geom/9407005. | MR | Zbl
,[39] Resolution of , preprint. | Zbl
,[40] Description of a class of superstring compactifications related to semi-simple Lie algebras, Comm. Math. Phys. 111 (1987), 247-274. | DOI | MR | Zbl
, and ,[41] J-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6, American Mathematical Society, Providence, 1994. | MR | Zbl
and ,[42] Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer. Math. Soc. 6 (1993), 223-247. | DOI | MR | Zbl
,[43] Picard-Fuchs equations and mirror maps for hypersurfaces, in [60], pp. 241-264. | MR | Zbl
,[44] Making enumerative predictions by means of mirror symmetry, alg-geom/9504013. | Zbl
,[45] Deformations of manifolds with torsion or negative canonical bundle, J. Alg. Geom. 1 (1992), 279-291. | MR | Zbl
,[46] The moduli space of 3-folds with K = 0 may nevertheless be irreducible, Math. Ann. 278 (1987), 329-334. | DOI | EuDML | MR | Zbl
,[47] On the generalization of Kummer surfaces, Jour. Diff. Geom. 30 (1983), 523-537. | DOI | MR | Zbl
,[48] On resolution of quotient singularity, preprint. | MR | Zbl
,[49] On Ricci flat 3-fold, Acta Math. Sinica (N. S.) 3 (1987), 256-288. | DOI | MR | Zbl
and ,[50] Topological sigma model and Donaldson type invariants in Gromov theory, preprint, 1993. | MR | Zbl
,[51] A mathematical theory of quantum cohomology, Math. Res. Lett. 1 (1994), 269-278. | DOI | MR | Zbl
and ,[52] The definitions of conformal field theory, in Links Between Geometry and Mathematical Physics, MPI preprint 87-58, 1987, pp. 13-17. | MR
,[53] Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Peterson-Weil metric, in "Mathematical Aspects of String Theory" (S.-T. Yau, ed.), World Scientific, Singapore, 1987, pp. 629-646. | MR | Zbl
,[54] Smoothing 3-folds with trivial canonical bundle and ordinary double points, in [60], pp. 458-479. | MR | Zbl
,[55] The Weil-Petersson geometry of the moduli space of SU(n ≥ 3) (Calabi-Yau) manifolds, I, Comm. Math. Phys. 126 (1989), 325-346. | DOI | Zbl
,[56] Miroirs et involutions sur les surfaces K3, Journées de Géométrie Algébrique d'Orsay (Juillet 1992), Astérisque, vol. 218, Société Mathématique de France, 1993, pp. 273-323. | MR | Zbl
,[57] Classification problems in topology V : On certain 6-manifolds, Invent. Math. 1 (1966), 355-374. | DOI | EuDML | Zbl
,[58] Mirror manifolds and topological field theory, in [60], 120-159. | MR | Zbl
,[59] On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation. I, Comm. Pure and Appl. Math. 31 (1978), 339-411. | DOI | MR | Zbl
,[60] Essays on Mirror Manifolds, International Press Co., Hong Kong (1992). | MR
(ed.),[tangent61] Compact three-dimensional Kähler manifolds with zero Ricci curvature, Symposium on Anomalies, Geometry, Topology (Chicago, Ill., 1985), 395-406. | MR | Zbl
,