论文标题
对希尔伯特计划的分类量子环形作用
A Categorical Quantum Toroidal Action on Hilbert Schemes
论文作者
论文摘要
我们将Nakajima的Heisenberg操作员的换倒$ P _ {\ pm 1} $及其在量子toroidal代数$ _ {q_1，q_1，q_2}（\ ddot {gl_1}）中无限的许多对应物。通过将我们的结果与Arxiv：1804.03645相结合，一个人获得了几何分类$ u_ {q_1，q_2}（\ ddot {gl_1}）$在Hilbert Shemes派生类别上的动作。我们的主要技术工具是通过最小模型程序的镜头对某些嵌套的希尔伯特方案进行详细的几何研究，它表明这些嵌套的希尔伯特方案是规范或半科学日志终端。
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. By combining our result with arxiv:1804.03645 , 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 semi-divisorial log terminal singularities.
