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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



$\mu _p$- and $\alpha _p$-actions on K3 surfaces in characteristic $p$

Author: Yuya Matsumoto
Journal: J. Algebraic Geom. 32 (2023), 271-322
Published electronically: August 4, 2022
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Abstract: We consider $\mu _p$- and $\alpha _p$-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic $p > 0$. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of $\mu _p$- and $\alpha _p$-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 $\mu _p$- or $\alpha _p$- 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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Additional Information

Yuya Matsumoto
Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan
MR Author ID: 1079656
ORCID: 0000-0002-7371-7956

Received by editor(s): January 31, 2021
Received by editor(s) in revised form: January 3, 2022
Published electronically: August 4, 2022
Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers 15H05738, 16K17560, and 20K14296.
Article copyright: © Copyright 2022 University Press, Inc.