A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES

被引：1

作者：

Zhao, Yu ^{[1
]}

机构：

[1] Univ Tokyo, Kavli IPMU, 5 Chome 1-5 Kashiwanoha, Kashiwa, Chiba 2778583, Japan

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2024年 / 23卷 / 02期

基金：

美国国家科学基金会; 日本学术振兴会;

关键词：

Derived category of coherent sheaves; Quantum group; Hilbert scheme; ELLIPTIC HALL ALGEBRA; K-THEORY; INTERSECTION; INSTANTONS; CURVE;

D O I：

10.1017/S1474748022000585

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We categorify the commutation of Nakajima's Heisenberg operators P(+/- 1 )and their infinitely many counterparts in the quantum toroidal algebra U-q1,(q2)(gl(1)) acting on the Grothendieck groups of Hilbert schemes from [10, 24, 26, 32]. By combining our result with [26], one obtains a geometric categorical U-q1,(q2)(gl(1)) action on the derived category of Hilbert schemes. Our main technical tool is a detailed geometric study of certain nested Hilbert schemes of triples and quadruples, through the lens of the minimal model program, by showing that these nested Hilbert schemes are either canonical or semidivisorial log terminal singularities.

引用

页码：897 / 940

页数：44

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