Gromov-Witten invariants for varieties with C* action

2015/05/06 by Anca Mustaţǎ, Mustata, Anca, Andrei Mustaţǎ +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1505.01471

openalex publication_date 2015/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any smooth projective variety with a C* action, we reduce the problem of computing its Gromov-Witten invariants to the similar problem for its fixed locus. Starting from the stacky version of variation of GIT for our variety, we construct the building blocks for the fixed loci of the moduli space of stable maps. We use this construction to compute their contribution to the virtual fundamental class.

Citations

• A virtual fundamental class construction for the moduli space of torus equivariant morphisms

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• On Gromov-Witten theory of projective bundles

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