Arc Spaces and Chiral Symplectic Cores
Arc Spaces and Chiral Symplectic Cores
复制标题
DOI：
10.4171/prims/57-3-3
复制
发表时间：
2018-02
影响因子：
1.2
通讯作者：
T. Arakawa;Anne Moreau
中科院分区：
文献类型：
--
作者：
T. Arakawa;Anne Moreau
我们引入了顶点Poisson簇中手征辛核的概念，它可以被看作Poisson簇中辛叶的类似物。作为一个应用程序，我们表明，任何quasi-lisse顶点代数是一个量子化的弧空间的相关品种，在这个意义上说，其减少奇异支持符合弧空间的相关品种。我们还证明了Slodowy切片弧空间的坐标环在其顶点Poisson中心上是自由的，并且后者与相应单李代数对偶弧空间的坐标环的顶点Poisson中心重合.
We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that any quasi-lisse vertex algebra is a quantization of the arc space of its associated variety, in the sense that its reduced singular support coincides with the arc space of its associated variety. We also show that the coordinate ring of the arc space of Slodowy slices is free over its vertex Poisson center, and the latter coincides with the vertex Poisson center of the coordinate ring of the arc space of the dual of the corresponding simple Lie algebra.