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September 2021 The wild McKay correspondence for cyclic groups of prime power order
Mahito Tanno, Takehiko Yasuda
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Illinois J. Math. 65(3): 619-654 (September 2021). DOI: 10.1215/00192082-9402078

Abstract

The 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. With this criterion, we obtain more examples of quotient varieties which are Kawamata log terminal (klt) but not Cohen–Macaulay.

Citation

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Mahito Tanno. Takehiko Yasuda. "The wild McKay correspondence for cyclic groups of prime power order." Illinois J. Math. 65 (3) 619 - 654, September 2021. https://doi.org/10.1215/00192082-9402078

Information

Received: 13 August 2020; Revised: 5 June 2021; Published: September 2021
First available in Project Euclid: 23 July 2021

Digital Object Identifier: 10.1215/00192082-9402078

Subjects:
Primary: 14E16
Secondary: 11S15, 14B05, 14E18, 14E22, 14G17, 14R20

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 3 • September 2021
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