Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
Authors:
Jun Li and Gang Tian
Journal:
J. Amer. Math. Soc. 11 (1998), 119-174
MSC (1991):
Primary 14D20
DOI:
https://doi.org/10.1090/S0894-0347-98-00250-1
MathSciNet review:
1467172
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we define the virtual moduli cycle of moduli spaces with perfect tangent-obstruction theory. The two interesting moduli spaces of this type are moduli spaces of vector bundles over surfaces and moduli spaces of stable morphisms from curves to projective varieties. As an application, we define the Gromov-Witten invariants of smooth projective varieties and prove all its basic properties.
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Additional Information
Jun Li
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
MR Author ID:
1093262
Email:
jli@gauss.stanford.edu
Gang Tian
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID:
220655
Email:
tian@math.mit.edu
Keywords:
Moduli space,
intersection theory,
invariant
Received by editor(s):
September 25, 1996
Received by editor(s) in revised form:
July 30, 1997
Additional Notes:
Both authors were supported in part by NSF grants, and the first author was also supported by an A. Sloan fellowship and Terman fellowship.
Article copyright:
© Copyright 1998
American Mathematical Society