The equivariant Gromov-Witten theory of P1

Annals of Mathematics

Volumn 163, Issue 2, 2006, Pages 561-605

  Okounkov, A ^a   Pandharipande, R ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746087123     PISSN: 0003486X     EISSN: 0003486X     Source Type: Journal    
DOI: 10.4007/annals.2006.163.561     Document Type: Article

References (30)

1. P. DI FRANCESO, 2-D quantum and topological gravities, matrix models, and integrable differential systems, in The Painlevé Property: One Century Later (R. Conte, ed.), 229-285, Springer-Verlag, New York, 1999.
2. C. L. DODGSON, The Mathematical Pamphlets of Charles Lutwidge Dodgson and Related Pieces (F. F. Abeles, ed.), Lewis Carroll Society of North America, Silver Spring, MD, 1994.
3. T. EGUCHI, K. HORI, and S.-K. YANG, Topological σ models and large-N matrix integral, Internat. J. Modern Phys. A 10 (1995), 4203-4224.
4. T. EGUCHI, K. HORI, and C.-S. XIONG, Quantum cohomology and Virasoro algebra, Phys. Lett. B402 (1997), 71-80.
5. 1 model and the large-N matrix integral, Modern Phys. Lett. A 9 (1994), 2893-2902.
6. T. EKEDAHL, S. LANDO, M. SHAPIRO, and A. VAINSHTEIN, Hurwitz numbers and intersections on moduli spaces of curves, Invent. Math. 146 (2001), 297-327.
7. B. FANTECHI and R. PANDHARIPANDE, Stable maps and branch divisors, Compositio Math. 130 (2002), 345-364.
8. A. GERASIMOV, A. MARSHAKOV, A. MIRONOV, A. MOROZOV, and A. ORLOV, Matrix models of two-dimensional gravity and Toda theory, Nucl. Phys. B 357 (1991), 565-618.
9. J.-L. GERVAIS and Y. MATSUO, W-geometries, Phys. Lett. B 274 (1992), 309-316.
10. E. GETZLER, The Toda conjecture, in Symplectic Geometry and Mirror Symmetry (Seoul, 2000), 51-79, World Sci. Publishing, River Edge, NJ (2001).
11. _, The equivariant Toda conjecture, Publ. Res. Inst. Math. Sci. 40 (2004), 507-536.
12. T. GRABER and R. PANDHARIPANDB, Localization of virtual classes, Invent. Math. 135 (1999), 487-518.
13. T. GRABER and R. VAKIL, Hodge integrals and Hurwitz numbers via virtual localization, Compositio Math. 135 (2003), 25-36.
14. C. ITZYKSON and J. B. ZUBER, Combinatorics of the modular group. II. The Kontsevich integral, Internat. J. Modern Phys. A 7 (1992), 5661-5705.
15. V. KAC, Infinite-Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge, 1985.
16. M. KONTSEVICH, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992), 1-23.
17. _, Enumeration of rational curves via torus actions, in The Moduli Space of Curves (R. Dijkgraaf, C. Faber, and G. van der Geer, eds.) (Texel Island, 1994), 335-368, Birkhäuser Boston, MA, 1995.
18. T. MIWA, M. JIMBO, and E. DATE, Solitons. Differential Equations, Symmetries and Infinite-Dimensional Algebras, Cambridge Tracts in Math. 135, Cambridge Univ. Press, Cambridge, 2000.
19. T. MUIR, The Theory of Determinants, 2nd edition, vol. 1, Macmillan, London, 1906.
20. A. OKOUNKOV, Infinite wedge and random partitions, Selecta Math. 7 (2001), 57-81.
21. _, Toda equations for Hurwitz numbers, Math. Res. Lett. 7 (2000), 447-453.
22. _, Generating functions for intersection numbers on moduli spaces of curves, Internat. Math. Res. Not. 2002, no. 18, 933-957.
23. A. OKOUNKOV and R. PANDHARIPANDE, Gromov-Witten theory, Hurwitz numbers, and matrix models, I, Ann. of Math. 163 (2006), 517-560.
24. _, Gromov-Witten theory, Hurwitz theory, and completed cycles; math.AG/0204305.
25. _, Virasoro constraints and descendents of odd classes in the Gromov-Witten theory of target curves, in preparation.
26. R. PANDHARIPANDE, The Toda equations and the Gromov-Witten theory of the Riemann sphere, Lett. Math. Phys. 53 (2000), 59-74.
27. T. TAKEBE, Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. I, Lett. Math. Phys. 21 (1991), 77-84,
28. T. TAKEBE, Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. part II, Publ. Res. Inst. Math. Sci. 27 (1991), 491-503.
29. K. UENO and K. TAKASAKI, Toda lattice hierarchy, in Group Reprsentations and Systems of Differential Equations (Tokyo, 1982), 1-95, Adv. Stud. Pure Math. 4, North-Holland, Amsterdam, 1984.
30. E. WITTEN, Two-dimensional gravity and intersection theory on moduli space, in Surveys in Differential Geometry (Cambridge, MA 1990), 243-310, Lehigh Univ., Bethlehem, PA, 1991.