Equivariant Gromov-Witten Invariants

International Mathematics Research Notices

Volumn , Issue 13, 1996, Pages

  Givental, Alexander B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842588046     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. P. Aspinwal and D. Morrison, Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262.
2. nl,...,nk, Comm. Math. Phys. 170 (1995), 503-528.
3. M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28.
4. V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994), 493-535.
5. V. V. Batyrev and D. van Straten, Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties, Comm. Math. Phys. 168 (1995), 493-533.
6. A. Beauville, Quantum cohomology of complete intersections, Mathematical Physics, Analysis, Geometry 2 (1995), 384-398.
7. K. Behrend and Yu. Manin, Stacks of stable maps and Gromov-Witten invariants, Duke Math. J. 85 (1996), 1-60.
8. 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 359 (1991), 21-74.
9. A. Collino, Some computations on the quantum cohomology product of a Fano hypersurface, informal draft.
10. R. Dijkgraaf, E. Verlinde, and H. Verlinde, "Notes on topological string theory and 2D quantum gravity" in String Theory and Quantum Gravity, ed. by M. Green et al., World-Scientific, Singapore, 1991, 91-156.
11. B. Dubrovin, "The geometry of 2D topological field theories" in Integrable Systems and Quantum Groups, Lecture Notes in Math. 1620, Springer-Verlag, Berlin, 1996, 120-348.
12. S. Fomin, S. Gelfand, and A. Postnikov, Quantum Schubert polynomials, preprint, 1996.
13. A. Givental, Homological geometry I: Projective hypersurfaces. Selecta Math. (N.S.) 1 (1995), 325-345.
14. _, "Homological geometry and mirror symmetry" in Proceedings of the International Congress of Mathematicians, 1994, Zürich, Birkhäuser, Basel, 1995, 472-480.
15. A. Givental and B. Kim, Quantum cohomology of flag manifolds and Toda lattices, Comm. Math. Phys. 168 (1994), 609-641.
16. M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
17. N-1, preprint, hepth/9511206.
18. B. Kim, Quantum cohomology of partial flag manifolds and a residue formula for their intersection pairings, IMRN (Internat. Math. Res. Notices) 1995, 1-16.
19. _, Equivariant quantum cohomology, to appear in IMRN (Internat. Math. Res. Notices).
20. _, Quantum cohomology of flag manifolds G/B and quantum Toda lattices, preprint, alg-geom/9607001, 1996.
21. M. Kontsevich, "Enumeration of rational curves via toric actions" in The Moduli Space of Curves, ed. by R. Dijkgraaf, C. Faber, and G. van der Geer, Progr. Math. 129, Birkhäuser, Boston, 1995, 335-368.
22. M. Kontsevich and Yu. Manin, Gromov-Witten classes, quantum cohomology and enumerative geometry, Comm. Math. Phys. 164 (1994), 525-562.
23. B. Kostant, Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight ρ, Selecta Math. (N.S.) 2 (1996), 43-91.
24. Yu. Manin, "Generating functions in algebraic geometry and summation over trees" in The Moduli Space of curves, ed. by R. Dijkgraaf, C. Faber, and G. van der Geer, Progr. Math. 129, Birkhäuser, Boston, 1995, 401-417.
25. D. McDuff and D. Salamon, J-Holomorphic Curves and Quantum Cohomology, Univ. Lecture Ser. 6, Amer. Math. Soc., Providence, 1994.
26. Ju. Moser, "Finitely many mass points on the line under the influence of an exponential potential - an integrable system" in Dynamical Systems, Theory and Applications, Lecture Notes in Phys. 38, Springer-Verlag, Berlin, 1975, 97-101.
27. A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras, Vol. I, Birkhäuser, Basel, 1990.
28. Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, Math. Res. Lett. 1 (1994), 269-278.
29. K. Saito, On periods of primitive integrals, I, preprint 412, Res. Inst. Math. Sci., 1982.
30. A. Schwarz, Sigma-models having supermanifolds as target spaces, preprint, Inst. Hautes Études Sci., 1995.