Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

Li, Jun; Tian, Gang

doi:10.1090/S0894-0347-98-00250-1

Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
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by Jun Li and Gang Tian

J. Amer. Math. Soc. 11 (1998), 119-174

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

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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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