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arXiv · 1602.06494

K-theoretic quasimap invariants and their wall-crossing

Hsian-Hua Tseng·Fenglong You
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Abstract

For each positive rational number $\epsilon$, we define $K$-theoretic $\epsilon$-stable quasimaps to certain GIT quotients $W\sslash G$. For $\epsilon>1$, 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 $\epsilon_1$ and $\epsilon_2$ 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.

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Hsian-Hua Tseng, Fenglong You. 2016-02-21. K-theoretic quasimap invariants and their wall-crossing. https://arxiv.org/abs/1602.06494

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