Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

Li, Jun¹ ; Tian, Gang²

¹ Department of Mathematics, Stanford University, Stanford, California 94305
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 119-174

Résumé

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.

Détail

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

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