A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES
A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES
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DOI：
10.1017/s1474748022000585
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发表时间：
2020-09
影响因子：
0.9
通讯作者：
Yu Zhao
中科院分区：
文献类型：
--
作者：
Yu Zhao
本文对文献[10，24，26，32]中的量子环形代数U_{q_1，q_2}（\ddot {gl_1}）$中Nakajima的Heisenberg算子P_{\pm 1}$及其无穷多个对应算子作用在Hilbert格式的Grothendieck群上的对易进行了分类.将我们的结果与文献[26]相结合，得到了Hilbert格式的导出范畴上的一个几何范畴U_{q_1，q_2}（\ddot {gl_1}）$作用.我们的主要技术工具是一个详细的几何研究的某些嵌套希尔伯特计划的三重和四重，通过透镜的最小模型程序，通过显示这些嵌套希尔伯特计划是典型的或semidivisorial日志终端奇点。
Abstract We categorify the commutation of Nakajima’s Heisenberg operators $P_{\pm 1}$ and their infinitely many counterparts in the quantum toroidal algebra $U_{q_1,q_2}(\ddot {gl_1})$ acting on the Grothendieck groups of Hilbert schemes from [10, 24, 26, 32]. By combining our result with [26], one obtains a geometric categorical $U_{q_1,q_2}(\ddot {gl_1})$ 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.