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arXiv · 2405.12020

Equivariantly normal varieties for diagonalizable group actions

Michel Brion
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Abstract

Given a finite group scheme $G$ over a field and a $G$-variety $X$, we obtain a criterion for $X$ to be $G$-normal in the sense of \cite{Br24}. When $G$ is diagonalizable, we describe the local structure of $G$-normal varieties in codimension $1$ and their dualizing sheaf. As an application, we obtain a version of the Hurwitz formula for $G$-normal varieties, where $G$ is linearly reductive.

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Michel Brion. 2024-05-20. Equivariantly normal varieties for diagonalizable group actions. https://arxiv.org/abs/2405.12020

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