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arXiv · 2101.08090

Discriminant groups of wild cyclic quotient singularities

Dino Lorenzini·Stefan Schröer
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Abstract

Let p be prime. We describe explicitly the resolution of singularities of several families of wild Z/pZ-quotient singularities in dimension two, including families that generalize the quotient singularities of type E_6, E_7, and E_8 from p=2 to arbitrary characteristics. We prove that for odd primes, any power of p can appear as the determinant of the intersection matrix of a wild Z/pZ-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.

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Dino Lorenzini, Stefan Schröer. 2021-01-20. Discriminant groups of wild cyclic quotient singularities. https://doi.org/10.2140/ant.2023.17.1017

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