2019/11/07 by Yang Zhou, Zhou, Yang · 1 citation
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1911.02745
openalex publication_date 2019/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove a wall-crossing formula for ε-stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold case. We prove that stability conditions in adjacent chambers give equivalent invariants, provided that both chambers are stable. In the case of genus-zero quasimaps with one marked point, we compute the invariants in the left-most stable chamber in terms of the small I-function. Using this we prove that the quasimap J-functions are on the Lagrangian cone of the Gromov--Witten theory. The proofs are based on virtual localization on a master space, obtained via some universal construction on the moduli of weighted curves. The fixed-point loci are in one-to-one correspondence with the terms in the wall-crossing formula.