Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau 3-folds

Advances in Theoretical and Mathematical Physics

Volumn 13, Issue 2, 2009, Pages 463-495

  Hosono, Shinobu ^a   Konishi, Yukiko ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350001623     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/ATMP.2009.v13.n2.a3     Document Type: Article

References (44)

1. 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. B 356 (1991), 21-74.
2. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories (with an appendix by S. Katz), Nucl. Phys. B 405 (1993), 279-304.
3. M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys. 165 (1994), 311-428.
4. M. Kontsevich, Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians (Zürich, 1994), Birkhäuser, 1995, 120-139.
5. T. Bridgeland and A. Maciocia, Complex surfaces with equivalent derived categories, Math. Zeit. 236 (2001), 677-697.
6. D. Orlov, Equivalences of derived categories and K3 surfaces, J. Math. Sci. 84 (1997), 1361-1381; math.AG/9606006.
7. K. Oguiso, K3 surfaces via almost-primes, Math. Res. Lett. 9 (2002), 47-63; math.AG/0110282.
8. S. Hosono, B.H. Lian, K. Oguiso and S.-T. Yau, Fourier-Mukai number of a K3 surface, in Algebraic Structures and Moduli Spaces', CRM Proc. Lecture Notes, Amer. Math. Soc., 38, Providence, RI, 2004, 177-192.
9. T. Bridgeland, Flops and derived categories, Invent. Math. 147 (3) (2002), 613-632.
10. L. Borisov and A. Caldararu, The Pfaffian-Grassmannian derived equivalence, math/0608404.
11. A. Kuznetsov, Homological projective duality for Grassmannians of lines, arXiv:math/0610957.
12. E.A. Rødland, The Pfaffian Calabi-Yau, its Mirror and their link to the Grassmannian G(2, 7), Compos. Math. 122 (2) (2000), 135-149; math.AG/9801092.
13. V. Batyrev, I. Ciocan-Fontanine, B. Kim and D. van Straten, Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians, Nucl. Phys. B 514 (1998), 640-666.
14. E.N. Tjøtta, Quantum cohomology of a Pfaffian Calabi-Yau variety: verifying mirror symmetry predictions, Compos. Math. 126 (1) (2001), 79-89.
15. A. Bertram, I. Ciocan-Fontanine and B. Kim, Two proofs of a conjecture of Hori and Vafa, Duke Math. J. 126 (2005), 101-136.
16. B. Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Math. 183 (1999), 71-99.
17. M. x. Huang, A. Klemm and S. Quackenbush, Topological string theory on compact Calabi-Yau: modularity and boundary conditions, hepth/ 0612125.
18. C. Faber and R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math. 139 (1) (2000), 173-199.
19. R.P. Thomas, A holomorphic casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Diff. Geom. 54 (2) (2000), 367-438.
20. R. Gopakumar and C. Vafa, M-Theory and Topological Strings-II, hep-th/9812127.
21. S. Yamaguchi and S.-T. Yau, Topological string partition functions as polynomials, JHEP 0407:047, 2004, hep-th/0406078.
22. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538.
23. 6, J. Alg. Geom. 13, (2004), 249-266.
24. B.R. Greene and M.R. Plesser, Duality in Calabi-Yau moduli space, Nucl. Phys. B 338 (1990) 15-37.
25. D.R. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces, in 'Essays on Mirror Manifolds', ed. S.-T. Yau, Internal Press, Hong Kong, 1992, 241-264.
26. C.F. Doran and J.W. Morgan, Mirror symmetry and integral variations of hodge structure underlying one parameter families of calabi-Yau threefolds, in "Mirror Symmetry V", 517-537, AMS/IP Stud. Adv. Math. 38, AMS, RI, 2006, math.AG/0505272.
27. C. Enckevort and D. van Straten, Monodromy calculations of fourth order equations of Calabi-Yau type, in "Mirror Symmetry V", 539-559 (see [26]), math.AG/0412539.
28. S. Mukai, Duality of polarized K3 surfaces, in 'New Trends in Algebraic Geometry (Warwick, 1996)', London Math. Soc., Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999, 311-326.
29. S. Hosono, B.H. Lian, K. Oguiso and S.-T. Yau, Autoequivalences of derived category of a K3 surface and monodromy transformations, J. Alg. Geom. 13 (2004), 513-545; math.AG/0201047.
30. B. Lian and S.-T. Yau, Arithmetic properties of mirror map and quantum coupling, Commun. Math. Phys. 176 (1996), 163-192.
31. P.S. Aspinwall, B. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993), 249-259.
32. J. Bass and A. Todorov, The analogue of the dedekind eta function for CY manifolds. I. J. Reine Angew. Math. 599 (2006), 61-96.
33. H. Fang, L. Zhiqin and K-I. Yoshikawa, Analytic torsion for Calabi-Yau Three-folds, math/0601411.
34. A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990), 163-180.
35. M. Aganatic, V. Bouchard and A. Klemm, Topological strings and (almost) modular forms, Commun. Math. Phys. 277 (2008) 771-819, hep-th/0607100.
36. M. Gunaydin, A. Neitzke and B. Pioline, Topological wave functions and heat equations, JHEP 0612:070, 2006, hep-th/0607200.
37. H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, hys. Rev. D 70 (2004), p. 106007; hep-th/ 0405146.
38. M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, 'The Moduli Space of Curves', Prog. Math., 129, Birkhäuser, Boston, MA, 1995, 165-172.
39. A.B. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices 13 (1996), 613-663.
40. B.H. Lian, K. Liu and S.-T. Yau, Mirror principle I, Asian J. Math. 1(4) (1997), 729-763; alg-geom/9712011.
41. A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995), 96-108.
42. S. Hosono, M.-H. Saito and A. Takahashi, Holomorphic anomaly equation and BPS state counting of rational elliptic surface, Adv. Theor. Math. Phys. 3 (1999), 177-208; hep-th/9901151.
43. S. Katz, A. Klemm and C. Vafa, M-thory, Topological strings and spinning black holes, Adv. Theor. Math. Phys. 3 (1999), 1445-1537; hepth/9910181.
44. S. Hosono, M.-H. Saito and A. Takahashi, Relative Lefschetz action and BPS state counting, Int. Math. Res. Notices 15 (2001), 783-816.