Localization of virtual classes
T. Graber, R. Pandharipande

TL;DR
This paper establishes a localization formula for virtual fundamental classes in torus-equivariant settings and applies it to express higher genus Gromov-Witten invariants of projective space as graph sums, extending known genus 0 results.
Contribution
It introduces a new localization formula for virtual classes and generalizes Gromov-Witten invariants computations to higher genus cases.
Findings
Derived a localization formula for virtual classes
Expressed higher genus Gromov-Witten invariants as graph sums
Computed excess integrals over higher genus multiple covers
Abstract
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology
