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2009 | 7 | 4 | 571-605
Tytuł artykułu

Homological Mirror Symmetry for manifolds of general type

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
571-605
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
autor
  • Algebra Section, Steklov Mathematical Institute RAS, Moscow, Russia, orlov@mi.ras.ru
  • Department of Mathematics and Statistics, Florida International University, Miami, USA, yotovm@gmail.com
Bibliografia
  • [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.2007.08.011[WoS][Crossref]
  • [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/s00222-006-0003-4[Crossref]
  • [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
  • [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
  • [5] Bondal A., Orlov D., Semiorthogonal decomposition for algebraic varieties, preprint available at http://arxiv.org/abs/alg-geom/9506012
  • [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-X[Crossref]
  • [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)90292-6[Crossref]
  • [8] Cox D., Katz S., Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs, 68, American Mathematical Society, Providence, RI, 1999
  • [9] Efimov A., Homological mirror symmetry for curves of higher genus, preprint available at http://arxiv.org/abs/0907.3903
  • [10] Fukaya K., Mirror symmetry of abelian varieties and multi-theta functions, J. Algebraic Geom., 2002, 11(3), 393–512
  • [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
  • [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
  • [13] Hori K., Vafa C., Mirror symmetry, preprint available at http://arxiv.org/abs/hep-th/0002222
  • [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)00026-3[Crossref]
  • [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/RM2004v059n05ABEH000772[Crossref]
  • [16] Kawamata Y., D-equivalence and K-equivalence, J. Differential Geom., 2002, 61(1), 147–171
  • [17] Kuznetsov A., Derived category of V 12 Fano threefolds, preprint available at http://arxiv.org/abs/math/0310008
  • [18] Mukai S., Non-Abelian Brill Noether theory and Fano 3 folds, preprint available at http://arxiv.org/abs/alg-geom/9704015
  • [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/10.2307/1970807[Crossref]
  • [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/BF02399195[Crossref]
  • [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
  • [22] Orlov D., Mirror symmetry for higher genus curves, Lectures at University of Miami, January 2008, IAS, March 2008
  • [23] Orlov D., Formal completions and idempotent completions of triangulated categories of singularities, preprint available at http://arxiv.org/abs/0901.1859 [WoS]
  • [24] Polishchuk A., Zaslow E., Categorical mirror symmetry: the elliptic curve, Adv. Theor. Math. Phys. 2, 1998, 2, 443–470
  • [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
  • [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
  • [27] Seidel P., Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics, 2008 [WoS]
  • [28] Seidel P., Homological mirror symmetry for the quartic surface, preprint available at http://arxiv.org/abs/math/0310414
  • [29] Seidel P., Homological mirror symmetry for the genus two curve, preprint available at http://arxiv.org/abs/0812.1171.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0056-x
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