The local gromov-witten theory of curves

Journal of the American Mathematical Society

Volumn 21, Issue 1, 2008, Pages 101-136

  Bryan, Jim ^a   Pandharipande, Rahul ^b   Faber, C ^c   Okounkov, A ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b PRINCETON UNIVERSITY   (United States)

^c ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60849086283     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-06-00545-5     Document Type: Article

References (30)

1. M. Aganagic, H. Ooguri, N. Saulina, and C. Vafa, Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings, Nuclear Phys. B 715 (2005), 304-348. MR2135642 (2006e:81264) (Pubitemid 40553613)
2. J. Bryan and T. Graber, The crepant resolution conjecture, math. AG/0610129.
3. J. Bryan and R. Pandharipande, On the rigidity of stable maps to Calabi-Yau threefolds, Proceedings of the BIRS workshop on the interaction of finite type and Gromov-Witten invariants, Geometry and Topology Monographs, Vol. 8 (2006), pp. 97-104.
4. J. Bryan and R. Pandharipande, BPS states of curves in Calabi-Yau 3-folds, Geom. Topol. 5 (2001), 287-318. MR1825668 (2002h:14092) (Pubitemid 39112998)
5. J. Bryan and R. Pandharipande, Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory, Duke J. 126 (2005), 369-396. MR2115262 (2005k:14117) (Pubitemid 40346176)
6. R. Dijkgraaf and E. Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990), 393-429, MR1048699 (91g:81133)
7. Y. Eliashberg, A. Givental, and H. Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000), 560-673. MR1826267 (2002e:53136) (Pubitemid 33261280)
8. C. Faber and R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math. 139 (2000), 173-199. MR1728879 (2000m:14057)
9. C. Faber and R. Pandharipande, Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier), Michigan Math. J. 48 (2000), 215-252. MR1786488 (2002e:14041)
10. D. Freed and F. Quinn, Chern-Simons theory with finite gauge group, Comm. Math. Phys. 156 (1993), 435-472. MR1240583 (94k:58023)
11. T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), 487-518. MR1666787 (2000h:14005)
12. E.-N. Ionel and T. Parker, Relative Gromov-Witten invariants, Ann. of Math. 157 (2003), 45-96. MR1954264 (2004a:53112) (Pubitemid 36325178)
13. E.-N. Ionel and T. Parker, The symplectic sum formula for Gromov-Witten invariants, Ann. of Math. 159 (2004), 935-1025. MR2113018 (2006b:53110) (Pubitemid 40306379)
14. J. Kock, Frobenius algebras and 2D topological quantum field theories, London Mathematical Society Student Texts 59, Cambridge University Press, Cambridge, 2004. MR2037238 (2005a:57028)
15. A.-M. Li and Y. Ruan, Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds, Invent. Math. 145 (2001), 151-218. MR1839289 (2002g:53158) (Pubitemid 33375439)
16. J. Li, Stable morphisms to singular schemes and relative stable morphisms, JDG 57 (2001), 509-578. MR1882667 (2003d:14066)
17. J. Li, A degeneration formula of GW-invariants, JDG 60 (2002), 199-293. MR1938113 (2004k:14096)
18. g. Invent. Math. 121 (1995), 411-419. MR1346214 (96g:14021)
19. I. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press, Oxford University Press, New York, 1995. MR1354144 (96h:05207)
20. D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory I (to appear in Comp. Math.), math. AG/0312059.
21. D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory II (to appear in Comp. Math.), math. AG/0406092.
22. A. Okounkov and R. Pandharipande, Hodge integrals and invariants of the unknot, Geom. Top. 8 (2004), 675-699. MR2057777 (2006c:14041) (Pubitemid 39113057)
23. A. Okounov and R. Pandharipande, Gromov-Witten theory, Hurwitz theory, and completed cycles, Annals of Math. (2) 163 (2006), 517-560. MR2199225 (Pubitemid 44077792)
24. A. Okounkov and R. Pandharipande, Quantum cohomology of the Hilbert scheme of points in the plane, math. AG/0411120.
25. A. Okounkov and R. Pandharipande, Local Donaldson-Thomas theory of curves, math. AG/0512573.
26. R. Pandharipande, Hodge integrals and degenerate contributions, Comm. Math. Phys. 208 (1999), 489-506. MR1729095 (2002k:14087)
27. R. Pandharipande, The Toda equation and the Gromov-Witten theory of the Riemann sphere, Lett. Math. Physics 53 (2000), 59-74. MR1799843 (2001j:14074)
28. R. Pandharipande, Three questions in Gromov-Witten theory, Proceedings of the International Congress of Mathematicians, Vol. II, 503-512, Higher Ed. Press, Beijing, 2002. MR1957060 (2003k:14069)
29. R. Thomas, A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, JDG 54 (2000), 367-438. MR1818182 (2002b:14049)
30. C. Vafa, Two dimensional Yang-Mills, black holes and topological strings, hep-th/0406058.