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

2014/09/22 by Andrei Mustaţǎ, Mustata, Andrei · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1409.6286

openalex publication_date 2014/09/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective variety with the action of the n dimensional torus. The article describes the moduli space of torus equivariant morphisms from stable toric varieties into X as the inverse limit of the GIT quotients of X and their flips when these spaces are enhanced with a naturally associated Deligne-Mumford stack structure. This description is used for constructing a class in the Chow group of the moduli space of dimension dim(X)-n which is invariant to equivariant deformations of X.

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