Higher genus quasimap wall-crossing for semi-positive targets

2013/08/29 by Ionuţ Ciocan-Fontanine, Ciocan-Fontanine, Ionut, Bumsig Kim +1 · 3 citations
Mathematics · #14D20 #14D23 #14N35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1308.6377

openalex publication_date 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In previous work (arXiv:1304.7056) 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 semi-positive, and prove them for semi-positive toric varieties, in particular for toric local Calabi-Yau targets. The proof also applies to local Calabi-Yau's associated to some non-abelian quotients.

Cited by

• Orbifold Quasimap Theory
• Irreducible components of moduli spaces of maps to smooth projective toric varieties in genus 0
• A short way of counting maps to hypersurfaces in Grassmannians

Related

• Wall-crossing in genus zero quasimap theory and mirror maps
• Quasimap wall-crossing for GIT quotients
• K-theoretic quasimap invariants and their wall-crossing
• K-theoretic quasimap wall-crossing
• Orbifold Quasimap Theory