Mirror symmetry in dimension 3
Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Talk no. 801, 19 p.
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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] P. S. Aspinwall, B. R. Green and D. R. Morrison, The monomial-divisor mirror map, Int. Math. Res. Notices (1993), 319-337, alg-geom/9309007. | DOI | MR | Zbl

[2] P. S. Aspinwall, B. R. Green and D. R. Morrison, 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

[3] P. S. Aspinwall and D. R. Morrison, Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262. | DOI | MR | Zbl

[4] V. V. Batyrev, 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] V. V. Batyrev and L. A. Borisov, Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, alg-geom/9402002. | Zbl

[6] V. V. Batyrev and D. Van Straten, Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toris varieties, alg-geom/ 9307010. | Zbl

[7] A. Beauville, Variétés kählériennes dont la première classe de Chern est nulle, Jour. Diff. Geom. 18 (1983), 755-782. | DOI | MR | Zbl

[8] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, with an appendix by S. Katz, Nucl. Phys. B405 (1993), 298-304. | DOI | MR | Zbl

[9] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Comm. Math. Phys. 165 (1994), 311-427. | DOI | MR | Zbl

[10] J. Bertin and D. Markushevich, Singularités quotients non abéliennes de dimension 3 et variétés de Bogomolov, Prépublication de l'Institut Fourier 216 (1992). | Zbl

[11] F. A. Bogomolov, Hamiltonian Kähler manifolds, Dokl. Akad. Nauk SSSR 245 (1978), 1101-1104. | MR | Zbl

[12] F. A. Bogomolov, On the decomposition of Kähler manifolds with trivial canonical class, Math. USSR Sbornik 22 (1974), 580-583. | DOI | MR | Zbl

[13] E. Calabi, The space of Kähler metrics, in Proceedings of the International Congress of Mathematicians (Amsterdam 1954), Vol. 2, pp. 206-207. | Zbl

[14] P. Candelas, E. Derrick and L. Parkes, Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B 407 (1993), 115-154. | DOI | MR | Zbl

[15] P. Candelas, C. A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. II. Three generation manifolds, Nucl. Phys. B306 (1988), 113-136. | DOI | MR

[16] P. Candelas, X.C. De La Ossa, A. Font, S. Katz and D. G. Morrison, Mirror symmetry for two-parameter models (I), Nucl. Phys. B416 (1994), 481-562, hep-th/9308083. | DOI | MR | Zbl

[17] P. Candelas, X.C. De La Ossa, P. S. Green and L. Parkes, 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

[18] P. Candelas, A. Font, S. Katz and D. G. Morrison, Mirror symmetry for two-parameter models - II, Nucl. Phys. B429 (1994), 624-674, hep-th/9403187. | DOI | MR | Zbl

[19] H. Clemens, Double solids, Adv. Math. 47 (1983), 107-230. | DOI | MR | Zbl

[20] L. J. Dixon, 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] G. Ellingsrud and S. A. Strømme, The number of twisted cubic curves on the general quintic threefold, Math. Scan., to appear. | EuDML | MR | Zbl

[22] R. Friedman, 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] K. Gawedzky, Conformal field theory, Séminaire Bourbaki 1988/89, n° 704, in Astérisque 177-178, pp. 95-126. | EuDML | Numdam | MR | Zbl

[24] B. R. Green, D. R. Morrison and M. R. Plesser, Mirror symmetry in higher dimension, hep-th/9402119.

[25] B. R. Green and M. R. Plesser, Duality in Calabi-Yau moduli space, Nucl. Phys. B338 (1990), 15-37. | DOI | MR

[26] P. S. Green and T. Hübsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys. 119 (1988), 431-441. | DOI | MR | Zbl

[27] P. Green, T. Hübsch and C. A. Lütken, All the Hodge numbers for all Calabi-Yau complete intersections, Class. Quantum Grav. 6 (1989), 105-124. | DOI | MR | Zbl

[28] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. | DOI | EuDML | MR | Zbl

[29] F. Hirzebruch, Some examples of threefolds with trivial canonical bundle, Gesammelte Abhandlungen, Bd. II, Springer-Verlag, 1987, pp. 757-770. | MR

[30] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Comm. Math. Phys. 167 (1995), 301-350, hep-th/9308122. | DOI | MR | Zbl

[31] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersections Calabi-Yau spaces, Nucl. Phys. B433 (1995), 501-544, hep-th/9406055. | DOI | MR | Zbl

[32] M. Jinzenji and M. Nagura, Mirror Symmetry and An Exact Calculation of N - 2 Point Correlation Function on Calabi-Yau Manifold embedded in ℂℙ N - 1 , hep-th/9409029. | DOI | Zbl

[33] S. Katz, 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] M. Kontsevich, Enumeration of rational curves via toric actions, MPI preprint 94-39, 1994, hep-th/9405035. | Zbl

[35] W. Lerche, C. Vafa and N. Warner, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B324 (1984), 427-474. | DOI | MR

[36] B. Lian and S.-T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, hep-th/9507151.

[37] A. Libgober and J. Teitelbaum, Lines on Calabi-Yau complete intersections, mirror symmetry and Picard-Fuchs equations, Intern. Math. Res. Not. 1 (1993), 29-39. | DOI | MR | Zbl

[38] Yu. Manin, Generating functions in algebraic geometry and sums over trees, MPI preprint, 1994, alg-geom/9407005. | MR | Zbl

[39] D. Markushevich, Resolution of C 3 / H 168 , preprint. | Zbl

[40] D. G. Markushevich, M. A. Olshanetsky and A. M. Perelomov, Description of a class of superstring compactifications related to semi-simple Lie algebras, Comm. Math. Phys. 111 (1987), 247-274. | DOI | MR | Zbl

[41] D. Mcduff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6, American Mathematical Society, Providence, 1994. | MR | Zbl

[42] D. Morrison, Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer. Math. Soc. 6 (1993), 223-247. | DOI | MR | Zbl

[43] D. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces, in [60], pp. 241-264. | MR | Zbl

[44] D. Morrison, Making enumerative predictions by means of mirror symmetry, alg-geom/9504013. | Zbl

[45] Z. Ran, Deformations of manifolds with torsion or negative canonical bundle, J. Alg. Geom. 1 (1992), 279-291. | MR | Zbl

[46] M. Reid, The moduli space of 3-folds with K = 0 may nevertheless be irreducible, Math. Ann. 278 (1987), 329-334. | DOI | EuDML | MR | Zbl

[47] S. S. Roan, On the generalization of Kummer surfaces, Jour. Diff. Geom. 30 (1983), 523-537. | DOI | MR | Zbl

[48] S. S. Roan, On c 1 = 0 resolution of quotient singularity, preprint. | MR | Zbl

[49] S. S. Roan and S.-T. Yau, On Ricci flat 3-fold, Acta Math. Sinica (N. S.) 3 (1987), 256-288. | DOI | MR | Zbl

[50] Y. Ruan, Topological sigma model and Donaldson type invariants in Gromov theory, preprint, 1993. | MR | Zbl

[51] Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, Math. Res. Lett. 1 (1994), 269-278. | DOI | MR | Zbl

[52] G. Segal, The definitions of conformal field theory, in Links Between Geometry and Mathematical Physics, MPI preprint 87-58, 1987, pp. 13-17. | MR

[53] G. Tian, 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] G. Tian, Smoothing 3-folds with trivial canonical bundle and ordinary double points, in [60], pp. 458-479. | MR | Zbl

[55] A. Todorov, 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] C. Voisin, 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] C. T. C. Wall, Classification problems in topology V : On certain 6-manifolds, Invent. Math. 1 (1966), 355-374. | DOI | EuDML | Zbl

[58] E. Witten, Mirror manifolds and topological field theory, in [60], 120-159. | MR | Zbl

[59] S.-T. Yau, 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] S.-T. Yau (ed.), Essays on Mirror Manifolds, International Press Co., Hong Kong (1992). | MR

[tangent61] S.-T. Yau, Compact three-dimensional Kähler manifolds with zero Ricci curvature, Symposium on Anomalies, Geometry, Topology (Chicago, Ill., 1985), 395-406. | MR | Zbl