Quasimap wall-crossing for GIT quotients

• 成果类型: Article
• 署名作者: Zhou, Yang
• 署名单位: Fudan University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01071-z
• 发表日期: 2022
• 页码: 581-660
• 关键词: gromov-witten invariants; stable quotients; mirror symmetry; MODULI SPACES; localization

摘要

In this paper, we prove a wall-crossing formula for epsilon-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.