Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians

Journal of the American Mathematical Society

Volumn 9, Issue 2, 1996, Pages 529-571

  Bertram, Aaron ^a   Daskalopoulos, Georgios ^b   Wentworth, Richard ^c  

^a UNIVERSITY OF UTAH   (United States)

^b BROWN UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030525856     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00190-7     Document Type: Article

References (31)

1. Atiyah, M. F. and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308 (1983), 523-615. MR 85k:14006
2. Arbarello, E., M. Cornalba, P. Griffiths, and J. Harris, Geometry of Algebraic Curves, Vol. I, Springer-Verlag, New York, Berlin, Heidelberg, 1985. MR 86h:14019
3. Bradlow, S. B., Special metrics and stability for holomorphic bundles with global sections, J. Diff. Geom. 33 (1991), 169-214. MR 91m:32031
4. Bradlow, S. B. and G. D. Daskalopoulos, Moduli of stable pairs for holomorphic bundles over Riemann surfaces, Int. J. Math. 2 (1991), 477-513. MR 93b:58026
5. Bradlow, S. B. and G. D. Daskalopoulos, Moduli of stable pairs for holomorphic bundles over Riemann surfaces II, Int. J. Math. 4 (1993), no. No. 6, 903-925. CMP 94:05
6. Bradlow, S., G. Daskalopoulos, and R. Wentworth, Birational equivalences of vortex moduli, Topology (to appear).
7. Bott, R. and L. Tu, Differential Forms in Algebraic Topology, Springer-Verlag, New York, Berlin, Heidelberg, 1982. MR 83i:57016
8. Bertram, A., Moduli of rank 2 vector bundles, theta divisors, and the geometry of curves on protective space, J. Diff. Geom. 35 (1992), 429-469. MR 93g:14037
9. Bruguières, A., The scheme of morphisms from an elliptic curve to a Grassmannian, Comp. Math. 63 (1987), 15-40. MR 88g:14009
10. Daskalopoulos, G. and K. Uhlenbeck, An application of transversality to the topology of the moduli space of stable bundles, Topology 34 (1994), 203-215.
11. Floer, A., Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575-611. MR 90e:58047
12. Fulton, W., Intersection Theory, Springer-Verlag, New York, Berlin, Heidelberg, 1984. MR 85k:14004
13. Gromov, M., Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 87j:53053
14. Gromov, M., Soft and hard symplectic geometry, in Proceedings of the International Congress of Mathematicians, Berkeley, 1986. MR 91c:53034
15. Griffiths, P. and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978. MR 80b:14001
16. Guillemin, V. and S. Sternberg, Birational equivalence in the symplectic category, Invent. Math. 97 (1989), 485-522. MR 90f:58060
17. Grothendieck, A., Techniques de construction et théorèmes d'existence en géometrie algébrique IV: Les schémas de Hilbert, Séminaire Bourbaki 221 (1960/61). MR 27:1339
18. Intriligator, K., Fusion residues, Mod. Phys. Lett. A6 (1991), 3543-3556. MR 92k:81180
19. Kirwan, F., On the homology of compactifications of moduli spaces of vector bundles over a Riemann surface, Proc. London Math. Soc. (3) 53 (1986), 237-266. MR 88e:14012
20. Kobayashi, S., Differential Geometry of Complex Vector Bundles, Princeton University Press, 1987. MR 89e:53100
21. Newstead, P.E., Introduction to Moduli Problems and Orbit Spaces, Tata Inst. Lectures 51 (1978), Springer-Verlag, Heidelberg. MR 81k:14002
22. Ruan, Y., Toplogical sigma model and Donaldson type invariants in Gromov theory, preprint, 1993.
23. Sacks, J. and K. K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math. 113 (1981), 1-24. MR 82f:58035
24. Strømme, S., On parameterized rational curves in Grassmann varieties, in Lecture Notes in Math. 1266, Springer-Verlag, New York, Berlin, Heidelberg, 1987. MR 88i:14020
25. Thaddeus, M., Conformal field theory and the cohomology of the moduli space of stable bundles, J. Diff. Geom. 35 (1992), 131-149. MR 93g:14017
26. Thaddeus, M., Stable pairs, linear systems, and the Verlinde formula, Invent. Math. 117 (1994), 317-353. MR 95e:14006
27. Tiwari, S., preprint.
28. Vafa, C., Topological mirrors and quantum rings, in "Essays on Mirror Manifolds", S.-T. Yau, ed., International Press, Hong Kong, 1992. MR 94c:81193
29. Wolfson, J., Gromov's compactness of pseudo-holomorphic curves and symplectic geometry, J. Diff. Geom. 28 (1988), 383-405. MR 89m:53058
30. Witten, E., Topological sigma models, Commun. Math. Phys. 118 (1988), 411-449. MR 90b:81080
31. Zagier, D., unpublished.