Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Gromov invariants for holomorphic maps
from Riemann surfaces to Grassmannians


Authors: Aaron Bertram, Georgios Daskalopoulos and Richard Wentworth
Journal: J. Amer. Math. Soc. 9 (1996), 529-571
MSC (1991): Primary 14C17; Secondary 14D20, 32G13
MathSciNet review: 1320154
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as ``Gromov invariants'') on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 14C17, 14D20, 32G13

Retrieve articles in all journals with MSC (1991): 14C17, 14D20, 32G13


Additional Information

Aaron Bertram
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: bertram@math.utah.edu

Georgios Daskalopoulos
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: daskal@gauss.math.brown.edu

Richard Wentworth
Affiliation: Department of Mathematics, University of California, Irvine, California 92717
Email: raw@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-96-00190-7
PII: S 0894-0347(96)00190-7
Received by editor(s): June 8, 1993
Received by editor(s) in revised form: November 22, 1994, and March 2, 1995
Additional Notes: The first author was supported in part by NSF Grant DMS-9218215.
The second author was supported in part by NSF Grant DMS-9303494.
The third author was supported in part by NSF Mathematics Postdoctoral Fellowship DMS-9007255.
Dedicated: Dedicated to Professor Raoul Bott on the occasion of his 70th birthday
Article copyright: © Copyright 1996 American Mathematical Society