3d mirror symmetry and quantum K-theory of hypertoric varieties
3d mirror symmetry and quantum K-theory of hypertoric varieties
复制标题
3d 镜面对称和超曲面簇的量子 K 理论
DOI：
10.1016/j.aim.2021.108081
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发表时间：
2022
影响因子：
1.7
通讯作者：
Zhou, Zijun
中科院分区：
文献类型：
--
作者：
Smirnov, Andrey;Zhou, Zijun
根据Aganagic-Okounkov [2]的思想，我们研究了由P1的拟映射的K-理论计数定义的超环面簇的顶点函数.本文证明了三维超环面镜对的两组q-差分方程是等价的，交换了Kähler参数和等变参数，偏振选择相反。三维镜对的顶点函数作为q-差分方程的解，满足特定的渐近条件，由椭圆稳定包络联系起来。各种概念的量子K-理论的hypertoric品种也进行了讨论。
Following the idea of Aganagic–Okounkov [2], we study vertex functions for hypertoric varieties, defined by K-theoretic counting of quasimaps from P 1. We prove the 3d mirror symmetry statement that the two sets of q-difference equations of a 3d hypertoric mirror pairs are equivalent to each other, with Kähler and equivariant parameters exchanged, and the opposite choice of polarization. Vertex functions of a 3d mirror pair, as solutions to the q-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes. Various notions of quantum K-theory for hypertoric varieties are also discussed.