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

MathSciNet review:
1467172

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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

Email:
jli@gauss.stanford.edu

**Gang Tian**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Email:
tian@math.mit.edu

DOI:
http://dx.doi.org/10.1090/S0894-0347-98-00250-1

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