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Localization of virtual classes

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arxiv alg-geom/9708001 v2 pith:SEUR2WDZ submitted 1997-08-01 alg-geom math.AG

Localization of virtual classes

T. Graber , R. Pandharipande This is my paper
classification alg-geom math.AG
keywords genusclasseshigherintegralslocalizationspacesvirtualapplication
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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  1. Virtual Jeffrey--Kirwan localisation

    math.AG 2026-07 accept novelty 7.0

    Virtual integrals over GIT quotients X//G equal Jeffrey–Kirwan residues of virtual integrals over T-fixed loci, for perfect obstruction theories and oriented (−2)-shifted symplectic structures, in cohomology and K-theory.