K-theoretic quasimap invariants and their wall-crossing

2016/02/21 by Hsian‐Hua Tseng, Tseng, Hsian-Hua, Fenglong You +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1602.06494

openalex publication_date 2016/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each positive rational number ε, we define K-theoretic ε-stable quasimaps to certain GIT quotients W\sslash G. For ε>1, this recovers the K-theoretic Gromov-Witten theory of W\sslash G introduced in more general context by Givental and Y.-P. Lee. For arbitrary ε₁ and ε₂ in different stability chambers, these K-theoretic quasimap invariants are expected to be related by wall-crossing formulas. We prove wall-crossing formulas for genus zero K-theoretic quasimap theory when the target W\sslash G admits a torus action with isolated fixed points and isolated one-dimensional orbits.

Cited by

• Quantum K-theory of toric varieties, level structures, and 3d mirror symmetry

Related

• Quasimap wall-crossing for GIT quotients
• Wall-crossing in genus zero quasimap theory and mirror maps
• K-theoretic quasimap wall-crossing
• Higher genus quasimap wall-crossing for semi-positive targets
• Gromov-Witten/Hurwitz wall-crossing