Pith. sign in

REVIEW 2 cited by

Localization of virtual classes

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

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

T. Graber , R. Pandharipande This is my paper · ORCID
classification alg-geommath.AG
keywords genusclasseshigherintegralslocalizationspacesvirtualapplication
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Relative Quasimaps and Tilting Module of $U(\mathfrak{gl}_n)$

    math.AG 2025-09 conditional novelty 8.0 of 10

    The equivariant cohomology of the moduli space of relative quasimaps to the flag variety carries a U(gl_n)-action whose specialized summand is, up to a known category equivalence, a tilting module.

  2. Virtual Jeffrey--Kirwan localisation

    math.AG 2026-07 accept novelty 7.0 of 10

    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.

Pith tools