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Discriminant groups of wild cyclic quotient singularities

Dino Lorenzini and Stefan Schröer

Vol. 17 (2023), No. 5, 1017–1068
Abstract

Let p be prime. We describe explicitly the resolution of singularities of several families of wild p-quotient singularities in dimension two, including families that generalize the quotient singularities of type E6, E7, and E8 from p = 2 to arbitrary characteristics. We prove that for p odd, any power of p can appear as the determinant of the intersection matrix of a wild p-quotient singularity. We also provide evidence towards the conjecture that in this situation one may choose the wild action to be ramified precisely at the origin.

Keywords
quotient singularity, cyclic, wild, discriminant group, resolution of singularities, Brieskorn singularity, Dynkin diagram
Mathematical Subject Classification
Primary: 13A50, 14B05, 14E15, 14J17
Milestones
Received: 19 February 2021
Revised: 11 March 2022
Accepted: 6 July 2022
Published: 9 May 2023
Authors
Dino Lorenzini
Department of Mathematics
University of Georgia
Athens, GA
United States
Stefan Schröer
Mathematisches Institut
Heinrich-Heine-Universität Düsseldorf
Düsseldorf
Germany

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