等变Hirzebruch类与商奇点的Molien级数
Equivariant Hirzebruch classes and Molien series of quotient singularities
摘要：
研究了商奇点类$\mathbb{C}^n/G$的Hirzebruch性质，其中$G$是有限矩阵群.主要结果表明，在适当的变量替换下，Hirzebruch类与$G$的Molien级数一致.一个crepant决议的Hirzebruch类可以被描述为专门的orbifold椭圆属由鲍里索夫和Libgober构建。它等于$G$元素的定心器的Molien级数的组合。这是麦凯信件的一个化身。结果示出了几个例子，特别是4维辛商奇点。
英文摘要：
We study properties of the Hirzebruch class of quotient singularities $\mathbb{C}^n/G$, where $G$ is a finite matrix group. The main result states that the Hirzebruch class coincides with the Molien series of $G$ under suitable substitution of variables. The Hirzebruch class of a crepant resolution can be described specializing the orbifold elliptic genus constructed by Borisov and Libgober. It is equal to the combination of Molien series of centralizers of elements of $G$. This is an incarnation of the McKay correspondence. The results are illustrated with several examples, in particular of 4-dimensional symplectic quotient singularities.
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