The Wild McKay Correspondence for Cyclic Groups of Prime Power Order
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929255157334016 |
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| author | Tanno, Mahito Yasuda, Takehiko |
| author_facet | Tanno, Mahito Yasuda, Takehiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_12048 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Wild McKay Correspondence for Cyclic Groups of Prime Power Order Tanno, Mahito Yasuda, Takehiko Algebraic Geometry Number Theory 14E16 (Primary) 11S15, 14B05, 14E18, 14E22, 14G17, 14R20 (Secondary) 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. |
| title | The Wild McKay Correspondence for Cyclic Groups of Prime Power Order |
| topic | Algebraic Geometry Number Theory 14E16 (Primary) 11S15, 14B05, 14E18, 14E22, 14G17, 14R20 (Secondary) |
| url | https://arxiv.org/abs/2006.12048 |