Mirror symmetry in dimension 3
Séminaire Bourbaki (1994-1995)
- Volume: 37, page 275-293
- ISSN: 0303-1179
Access Full Article
topHow to cite
topKontsevich, Maxim. "Mirror symmetry in dimension 3." Séminaire Bourbaki 37 (1994-1995): 275-293. <http://eudml.org/doc/110202>.
@article{Kontsevich1994-1995,
author = {Kontsevich, Maxim},
journal = {Séminaire Bourbaki},
keywords = {mirror symmetry; Calabi-Yau manifolds; string theories; variation of Hodge structures; holomorphic anomaly equations},
language = {eng},
pages = {275-293},
publisher = {Société Mathématique de France},
title = {Mirror symmetry in dimension 3},
url = {http://eudml.org/doc/110202},
volume = {37},
year = {1994-1995},
}
TY - JOUR
AU - Kontsevich, Maxim
TI - Mirror symmetry in dimension 3
JO - Séminaire Bourbaki
PY - 1994-1995
PB - Société Mathématique de France
VL - 37
SP - 275
EP - 293
LA - eng
KW - mirror symmetry; Calabi-Yau manifolds; string theories; variation of Hodge structures; holomorphic anomaly equations
UR - http://eudml.org/doc/110202
ER -
References
top- [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. Zbl0798.14030MR1253648
- [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. Zbl0899.32006MR1274435
- [3] P.S. Aspinwall and D.R. Morrison, Topological field theory and rational curves, Comm. Math. Phys.151 (1993), 245-262. Zbl0776.53043MR1204770
- [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. Zbl0829.14023MR1269718
- [5] V.V. Batyrev and L.A. Borisov, Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, alg-geom/9402002.
- [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. Zbl0843.14016
- [7] A. Beauville, Variétés kählériennes dont la première classe de Chern est nulle, Jour. Diff. Geom.18 (1983), 755-782. Zbl0537.53056MR730926
- [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. Zbl0908.58074MR1240687
- [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. Zbl0815.53082MR1301851
- [10] J. Bertin and D. Markushevich, Singularités quotients non abéliennes de dimension 3 et variétés de Bogomolov, Prépublication de l'Institut Fourier216 (1992).
- [11] F.A. Bogomolov, Hamiltonian Kähler manifolds, Dokl. Akad. Nauk SSSR245 (1978), 1101-1104. Zbl0418.53026MR514769
- [12] F.A. Bogomolov, On the decomposition of Kähler manifolds with trivial canonical class, Math. USSR Sbornik22 (1974), 580-583. Zbl0304.32016MR338459
- [13] E. Calabi, The space of Kähler metrics, in Proceedings of the International Congress of Mathematicians (Amsterdam1954), Vol. 2, pp. 206-207.
- [14] P. Candelas, E. Derrick and L. Parkes, Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B407 (1993), 115-154. Zbl0899.32011MR1242064
- [15] P. Candelas, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. II. Three generation manifolds, Nucl. Phys. B306 (1988), 113-136. MR952965
- [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. Zbl0899.14017MR1274436
- [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. Zbl1098.32506MR1191420
- [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. Zbl1020.32506
- [19] H. Clemens, Double solids, Adv. Math.47 (1983), 107-230. Zbl0509.14045MR690465
- [20] L.J. Dixon, Some world-sheet properties of superstring compactifications, on orbifolds and otherwise, Superstrings, Unified Theories and Cosmology1987 (G. Furlan et al. eds.), World Scientific, Singapore, 1988, pp. 67-126. MR1104035
- [21] G. Ellingsrud and S.A. Strømme, The number of twisted cubic curves on the general quintic threefold, Math. Scan., to appear. Zbl0863.14033MR1345086
- [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. Zbl0753.14035MR1141199
- [23] K. Gawedzky, Conformal field theory, Séminaire Bourbaki1988/89, n° 704, in Astérisque177-178, pp. 95-126. Zbl0699.53085MR1040570
- [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. MR1059831
- [26] P.S. Green and T. Hübsch, Connecting moduli spaces of Calabi-Yau threefolds, Comm. Math. Phys.119 (1988), 431-441. Zbl0684.53077MR969210
- [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. Zbl0657.53063MR979162
- [28] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math.82 (1985), 307-347. Zbl0592.53025MR1554036
- [29] F. Hirzebruch, Some examples of threefolds with trivial canonical bundle, Gesammelte Abhandlungen, Bd. II, Springer-Verlag, 1987, pp. 757-770.
- [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. Zbl0814.53056MR1316509
- [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. Zbl1020.32508MR1319280
- [32] M. Jinzenji and M. Nagura, Mirror Symmetry and An Exact Calculation of N—2 Point Correlation Function on Calabi-Yau Manifold embedded in CPN-1, hep-th/9409029. Zbl1044.14510
- [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. Zbl0839.14043MR1302954
- [34] M. Kontsevich, Enumeration of rational curves via toric actions, MPI preprint 94-39, 1994, hep-th/9405035.
- [35] W. Lerche, C. Vafa and N. Warner, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B324 (1984), 427-474. MR1025424
- [36] B. Lian and S.-T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I, hep-th/9507151. Zbl0957.32501
- [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. Zbl0789.14005MR1201748
- [38] Yu. Manin, Generating functions in algebraic geometry and sums over trees, MPI preprint, 1994, alg-geom/9407005. MR1363064
- [39] D. Markushevich, Resolution of C3/H168, preprint.
- [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. Zbl0628.53065MR899851
- [41] D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6, American Mathematical Society, Providence, 1994. Zbl0809.53002MR1286255
- [42] D. Morrison, Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer. Math. Soc.6 (1993), 223-247. Zbl0843.14005MR1179538
- [43] D. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces, in [60], pp. 241-264. Zbl0841.32013MR1191426
- [44] D. Morrison, Making enumerative predictions by means of mirror symmetry, alg-geom/9504013.
- [45] Z. Ran, Deformations of manifolds with torsion or negative canonical bundle, J. Alg. Geom.1 (1992), 279-291. Zbl0818.14003MR1144440
- [46] M. Reid, The moduli space of 3-folds with K = 0 may nevertheless be irreducible, Math. Ann.278 (1987), 329-334. Zbl0649.14021MR909231
- [47] S.S. Roan, On the generalization of Kummer surfaces, Jour. Diff. Geom.30 (1983), 523-537. Zbl0661.14031MR1010170
- [48] S.S. Roan, On c1 = 0 resolution of quotient singularity, preprint. Zbl0856.14005MR1284568
- [49] S.S. Roan and S.-T. Yau, On Ricci flat 3-fold, Acta Math. Sinica (N. S.)3 (1987), 256-288. Zbl0649.14024MR916270
- [50] Y. Ruan, Topological sigma model and Donaldson type invariants in Gromov theory, preprint, 1993. MR1390655
- [51] Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, Math. Res. Lett.1 (1994), 269-278. Zbl0860.58006MR1266766
- [52] G. Segal, The definitions of conformal field theory, in Links Between Geometry and Mathematical Physics, MPI preprint 87-58, 1987, pp. 13-17. MR981378
- [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. Zbl0696.53040MR915841
- [54] G. Tian, Smoothing 3-folds with trivial canonical bundle and ordinary double points, in [60], pp. 458-479. Zbl0829.32012MR1191437
- [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. Zbl0688.53030
- [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. Zbl0818.14014MR1265318
- [57] C.T.C. Wall, Classification problems in topology V : On certain 6-manifolds, Invent. Math.1 (1966), 355-374. Zbl0149.20601
- [58] E. Witten, Mirror manifolds and topological field theory, in [60], 120-159. Zbl0834.58013MR1191422
- [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. Zbl0369.53059MR480350
- [60] S.-T. Yau (ed.), Essays on Mirror Manifolds, International Press Co., Hong Kong (1992). Zbl0816.00010MR1191418
- [tangent61] S.-T. Yau, Compact three-dimensional Kähler manifolds with zero Ricci curvature, Symposium on Anomalies, Geometry, Topology (Chicago, Ill., 1985), 395-406. Zbl0643.53050MR850873
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.