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arXiv · 1812.03466

$μ_p$- and $α_p$-actions on K3 surfaces in characteristic $p$

Yuya Matsumoto
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Abstract

We consider $μ_p$- and $α_p$-actions on RDP K3 surfaces (K3 surfaces with rational double point singularities allowed) in characteristic $p > 0$. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of $μ_p$- and $α_p$-actions are analogous to those of $\mathbb{Z}/l\mathbb{Z}$-actions (for primes $l \neq p$) and $\mathbb{Z}/p\mathbb{Z}$-quotients respectively. We also show that conversely an RDP K3 surface with a certain configuration of singularities admits a $μ_p$- or $α_p$- or $\mathbb{Z}/p\mathbb{Z}$-covering by a "K3-like" surface, which is often an RDP K3 surface but not always, as in the case of the canonical coverings of Enriques surfaces in characteristic $2$.

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Yuya Matsumoto. 2021-01-31. $μ_p$- and $α_p$-actions on K3 surfaces in characteristic $p$. https://doi.org/10.1090/jag%2F804

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