Homological Mirror Symmetry for manifolds of general type

[1] Abouzaid M., On the Fukaya categories of higher genus surfaces, Adv. Math., 2008, 217(3), 1192–1235 http://dx.doi.org/10.1016/j.aim.2007.08.01110.1016/j.aim.2007.08.011Search in Google Scholar

[2] Auroux D., Katzarkov L., Orlov D., Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves, Invent. Math., 2006, 166(3), 537–582 http://dx.doi.org/10.1007/s00222-006-0003-410.1007/s00222-006-0003-4Search in Google Scholar

[3] Auroux D., Katzarkov L., Orlov D., Mirror symmetry for weighted projective planes and their noncommutative deformations, preprint available at http://arxiv.org/abs/math/0404281 Search in Google Scholar

[4] Bondal A., Kapranov M., Framed triangulated categories, Mat. Sb., 1990, 181(5), 669–683 (in Russian), English translation: Math. USSR-Sb., 1991, 70(1), 93–107 10.1070/SM1991v070n01ABEH001253Search in Google Scholar

[5] Bondal A., Orlov D., Semiorthogonal decomposition for algebraic varieties, preprint available at http://arxiv.org/abs/alg-geom/9506012 Search in Google Scholar

[6] Bridgeland T., King A., Reid M., The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc., 2001, 14(3), 535–554 http://dx.doi.org/10.1090/S0894-0347-01-00368-X10.1090/S0894-0347-01-00368-XSearch in Google Scholar

[7] Candelas P., de la Ossa X., Green P., Parkes L., A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B, 1991, 359(1), 21–74 http://dx.doi.org/10.1016/0550-3213(91)90292-610.1016/0550-3213(91)90292-6Search in Google Scholar

[8] Cox D., Katz S., Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs, 68, American Mathematical Society, Providence, RI, 1999 10.1090/surv/068Search in Google Scholar

[9] Efimov A., Homological mirror symmetry for curves of higher genus, preprint available at http://arxiv.org/abs/0907.3903 Search in Google Scholar

[10] Fukaya K., Mirror symmetry of abelian varieties and multi-theta functions, J. Algebraic Geom., 2002, 11(3), 393–512 10.1090/S1056-3911-02-00329-6Search in Google Scholar

[11] Fukaya K., Oh Y.-G., Ohta H., Ono K., Lagrangian intersection Floer theory — anomaly and obstruction, preprint available at http://www.math.kyoto-u.ac.jp/fukaya/fukaya.html Search in Google Scholar

[12] Hori K., Katz S., Klemm A., Pandharipande R., Thomas R., Vafa C., Vakil R., Zaslow E., Mirror symmetry, Volume 1, Clay Mathematics Monographs, American Mathematical Society, Providence, RI, 2003 Search in Google Scholar

[13] Hori K., Vafa C., Mirror symmetry, preprint available at http://arxiv.org/abs/hep-th/0002222 Search in Google Scholar

[14] Kapustin A., Orlov D., Remarks on A-branes, mirror symmetry, and the Fukaya category, J. Geom. Phys., 2003, 48(1), 84–99 http://dx.doi.org/10.1016/S0393-0440(03)00026-310.1016/S0393-0440(03)00026-3Search in Google Scholar

[15] Kapustin A., Orlov D., Lectures on mirror symmetry, derived categories, and D-branes, Russian Math. Surveys, 2004, 59(5), 907–940 http://dx.doi.org/10.1070/RM2004v059n05ABEH00077210.1070/RM2004v059n05ABEH000772Search in Google Scholar

[16] Kawamata Y., D-equivalence and K-equivalence, J. Differential Geom., 2002, 61(1), 147–171 10.4310/jdg/1090351323Search in Google Scholar

[17] Kuznetsov A., Derived category of V 12 Fano threefolds, preprint available at http://arxiv.org/abs/math/0310008 Search in Google Scholar

[18] Mukai S., Non-Abelian Brill Noether theory and Fano 3 folds, preprint available at http://arxiv.org/abs/alg-geom/9704015 Search in Google Scholar

[19] Narasimhan M.S., Ramanan S., Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2), 1969, 89, 14–51 http://dx.doi.org/10.2307/197080710.2307/1970807Search in Google Scholar

[20] Orlov D., Equivalences of derived categories and K3 surfaces, J. Math. Sci. (New York), 1997, 84(5), 1361–1381 http://dx.doi.org/10.1007/BF0239919510.1007/BF02399195Search in Google Scholar

[21] Orlov D., Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Tr. Mat. Inst. Steklova, 2004, 246, Algebr. Geom. Metody, Svyazi i Prilozh., 240–262, English translation: Proc. Steklov Inst. Math., 2004, 3, 227–248 Search in Google Scholar

[22] Orlov D., Mirror symmetry for higher genus curves, Lectures at University of Miami, January 2008, IAS, March 2008 Search in Google Scholar

[23] Orlov D., Formal completions and idempotent completions of triangulated categories of singularities, preprint available at http://arxiv.org/abs/0901.1859 Search in Google Scholar

[24] Polishchuk A., Zaslow E., Categorical mirror symmetry: the elliptic curve, Adv. Theor. Math. Phys. 2, 1998, 2, 443–470 10.4310/ATMP.1998.v2.n2.a9Search in Google Scholar

[25] Seidel P., More about vanishing cycles and mutation, Symplectic geometry and mirror symmetry (Seoul, 2000), 429–465, World Sci. Publ., River Edge, NJ, 2001 10.1142/9789812799821_0012Search in Google Scholar

[26] Seidel P., Fukaya categories and deformations, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 351–360, Higher Ed. Press, Beijing, 2002 Search in Google Scholar

[27] Seidel P., Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics, 2008 10.4171/063Search in Google Scholar

[28] Seidel P., Homological mirror symmetry for the quartic surface, preprint available at http://arxiv.org/abs/math/0310414 Search in Google Scholar

[29] Seidel P., Homological mirror symmetry for the genus two curve, preprint available at http://arxiv.org/abs/0812.1171. Search in Google Scholar