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Pré-Publication, Document De Travail Année : 2019

K3 surfaces with maximal finite automorphism groups containing $M_{20}$

Résumé

It was shown by Mukai that the maximum order of a finite group acting faithfully and symplectically on a K3 surface is $960$ and that the group is isomorphic to the group $M_{20}$. Then Kondo showed that the maximum order of a finite group acting faithfully on a K3 surface is $3\,840$ and this group contains the Mathieu group $M_{20}$ with index four. Kondo also showed that there is a unique K3 surface on which this group acts faithfully, which is the Kummer surface $\Km(E_i\times E_i)$. In this paper we describe two more K3 surfaces admitting a big finite automorphism group of order $1\,920$, both groups contains $M_{20}$ as a subgroup of index 2. We show moreover that these two groups and the two K3 surfaces are unique. This result was shown independently by S. Brandhorst and K. Hashimoto in a forthcoming paper, with the aim of classifying all the finite groups acting faithfully on K3 surfaces with maximal symplectic part.
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Dates et versions

hal-02317043 , version 1 (15-10-2019)
hal-02317043 , version 2 (25-05-2020)

Identifiants

  • HAL Id : hal-02317043 , version 1

Citer

Cédric Bonnafé, Alessandra Sarti. K3 surfaces with maximal finite automorphism groups containing $M_{20}$. 2019. ⟨hal-02317043v1⟩
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