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arXiv · 1710.07158

On $μ_{n}$-actions on K3 surfaces in positive characteristic

Yuya Matsumoto
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Abstract

In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e.\ automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group schemes $μ_{n}$ on K3 surfaces (possibly with rational double point singularities) in characteristic $p$, where $n$ may be divisible by $p$. We introduce the notion of symplecticness of such actions, and we show that symplectic $μ_{n}$-actions have similar properties, such as possible orders, fixed loci, and quotients, to symplectic automorphisms of order $n$ in characteristic $0$. We also study local $μ_n$-actions on rational double points.

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Yuya Matsumoto. 2022-02-20. On $μ_{n}$-actions on K3 surfaces in positive characteristic. https://doi.org/10.1017/nmj.2022.20

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