野循环商奇点的判别群
Discriminant groups of wild cyclic quotient singularities
AI总结：
本文显式描述二维野循环商奇点的消解，证明奇素数下 p 的任意幂可为相交矩阵行列式，并支持野作用仅在原点分歧的猜想。
摘要：
设 p 为素数。我们显式描述二维中若干族野 Z/pZ-商奇点的奇点消解，包括将类型 E_6、E_7 和 E_8 的商奇点从 p=2 推广到任意特征的族。我们证明对于奇素数，p 的任意幂可以作为野 Z/pZ-商奇点的相交矩阵的行列式出现。我们还为此情形下可选择野作用恰好仅在原点分歧的猜想提供了证据。
英文摘要：
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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