Localization of virtual classes

Details Localization of virtual classes Localization of virtual classes

1997-08-01

arxiv.org/abs/alg-geom/9708001v2

Mathematics

Algebraic Geometry

29 pages, LaTeX2e, General revision including error corrections

Scientific paper

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed.

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