Extensions of maximal symplectic actions on K3 surfaces

Brandhorst, Simon; Hashimoto, Kenji

doi:10.5802/ahl.88

Brandhorst, Simon ¹; Hashimoto, Kenji ²

¹ Fakultät für Mathematik und Informatik, Universität des Saarlandes, Campus E2.4, 66123 Saarbrücken, (Germany)
² Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Maguro-ku, Tokyo, 153-8914, (Japan)

Annales Henri Lebesgue, Volume 4 (2021), pp. 785-809.

Abstract
Résumé

We classify pairs $(X, G)$ consisting of a complex K3 surface $X$ and a finite group $G \leq Aut (X)$ such that the subgroup $G_{s} ⪇ G$ consisting of symplectic automorphisms is among the $11$ maximal symplectic ones as classified by Mukai.

Nous classifions les paires $(X, G)$ formées d’une surface K3 complexe $X$ et d’un groupe fini $G \leq Aut (X)$ pour lesquelles le sous-groupe $G_{s} ⪇ G$ des automorphismes symplectiques appartient aux $11$ sous-groupes symplectiques maximaux classifiés par Mukai.

Received: 2020-05-04
Revised: 2020-10-07
Accepted: 2020-11-23
Published online: 2021-08-26

DOI: 10.5802/ahl.88

Classification: 14J28, 14J50
Mots-clés : K3 surface, automorphism, Mathieu group

Author's affiliations:

Brandhorst, Simon ¹; Hashimoto, Kenji ²

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     title = {Extensions of maximal symplectic actions on {K3} surfaces},
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     url = {http://www.numdam.org/articles/10.5802/ahl.88/}
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Brandhorst, Simon; Hashimoto, Kenji. Extensions of maximal symplectic actions on K3 surfaces. Annales Henri Lebesgue, Volume 4 (2021), pp. 785-809. doi : 10.5802/ahl.88. http://www.numdam.org/articles/10.5802/ahl.88/

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