Localization of virtual classes

1997/08/01 by Graber, T., Pandharipande, R. · 12 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9708001

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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• The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants
• A categorical perspective on non-abelian localization
• Computations in equivariant Gromov-Witten theory of GKM spaces
• Relative Quasimaps and Tilting Module of U(\mathfrakgl_n)
• Hochschild-Kostant-Rosenberg isomorphism for derived Deligne-Mumford stacks
• Virtual invariants of Quot schemes of points on threefolds
• The refined local Donaldson-Thomas theory of curves
• BPS polynomials and Welschinger invariants
• On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces

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