Higher genus quasimap wall-crossing for semipositive targets

Ionuţ Ciocan-Fontanine, Bumsig Kim

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18 Scopus citations

Abstract

In previous work we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is semipositive, and prove them for semipositive toric varieties, in particular for toric local Calabi-Yau targets. The proof also applies to local Calabi-Yau's associated to some nonabelian quotients.

Original languageEnglish (US)
Pages (from-to)2051-2102
Number of pages52
JournalJournal of the European Mathematical Society
Volume19
Issue number7
DOIs
StatePublished - 2017

Bibliographical note

Funding Information:
The research of I.C.-F. was partially supported by the NSA grant H98230-11-1-0125 and the NSF grant DMS-1305004. The research of B.K. was partially supported by NRF- 2007-0093859. In addition, I.C-F. thanks KIAS for financial support, excellent working conditions, and an inspiring research environment. The authors thank the referee for helpful suggestions and Hyeonho Lho for pointing out an error in an earlier version.

Keywords

  • Gromov-Witten invariants
  • Mirror symmetry
  • Quasimaps

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