$K$-theoretic quasimap wall-crossing

Abstract

In this paper, we prove a K-theoretic wall-crossing formula for $\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0 mirror theorem for quantum K-theory with level structure by Ruan-Zhang. The proofs are based on K-theoretic virtual localization on the master space introduced by the second author in arXiv:1911.02745.

arXiv comment68 pages

References in corpus (21)

• The moduli space of stable quotients
• Moduli stacks of stable toric quasimaps
• Baxter Q-operator from quantum K-theory
• Mirror Theorem for Elliptic Quasimap Invariants
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Quantum K-Theory of Calabi-Yau Manifolds
• Permutation-equivariant quantum K-theory V. Toric $q$-hypergeometric functions
• Permutation-equivariant quantum K-theory II. Fixed point localization
• 3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians
• Permutation-equivariant quantum K-theory VIII. Explicit reconstruction
• Quantum K-theory of grassmannians and non-abelian localization
• On the WDVV-equation in quantum K-theory
• K-theoretic quasimap invariants and their wall-crossing
• Quasimap wall-crossing for GIT quotients
• Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry
• Permutation-equivariant quantum K-theory IV. $D_q$-modules
• Quantum orbifold Hirzebruch-Riemann-Roch theorem in genus zero
• Permutation-equivariant quantum K-theory VI. Mirrors
• Permutation-equivariant quantum K-theory III. Lefschetz' formula on ${\overline{M}}_{0,n}/S_n$ and adelic characterization
• Permutation-equivariant quantum K-theory XI. Quantum Adams-Riemann-Roch
• Permutation-equivariant quantum K-theory VII. General theory