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arXiv · 2006.12048

The Wild McKay Correspondence for Cyclic Groups of Prime Power Order

Mahito Tanno·Takehiko Yasuda
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Abstract

The $\boldsymbol{v}$-function is a key ingredient in the wild McKay correspondence. In this paper, we give a formula to compute it in terms of valuations of Witt vectors, when the given group is a cyclic group of prime power order. We apply it to study singularities of a quotient variety by a cyclic group of prime square order. We give a criterion whether the stringy motive of the quotient variety converges or not. Furthermore, if the given representation is indecomposable, then we also give a simple criterion for the quotient variety being terminal, canonical, log canonical, and not log canonical.

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Mahito Tanno, Takehiko Yasuda. 2020-06-22. The Wild McKay Correspondence for Cyclic Groups of Prime Power Order. https://doi.org/10.1215/00192082-9402078

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