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Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians
Author(s):
Aaron
Bertram;
Georgios
Daskalopoulos;
Richard
Wentworth
Journal:
J. Amer. Math. Soc.
9
(1996),
529-571.
MSC (1991):
Primary 14C17;
Secondary 14D20, 32G13
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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.
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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