The Wild McKay Correspondence for Cyclic Groups of Prime Power Order
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.12048
 Bibcode:
 2020arXiv200612048T
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14E16 (Primary) 11S15;
 14B05;
 14E18;
 14E22;
 14G17;
 14R20 (Secondary)
 EPrint:
 27 pages