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arXiv · 1602.02436

Equivariant Hirzebruch classes and Molien series of quotient singularities

Maria Donten-Bury·Andrzej Weber
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Abstract

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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Maria Donten-Bury, Andrzej Weber. 2016-02-07. Equivariant Hirzebruch classes and Molien series of quotient singularities. https://arxiv.org/abs/1602.02436

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