K3 surfaces with maximal finite automorphism groups containing M 20
| Autor: | Alessandra Sarti, Cédric Bonnafé |
|---|---|
| Přispěvatelé: | Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Applications (LMA-Poitiers), Université de Poitiers-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0010,GeRepMod,Méthodes géométriques en théorie des représentations modulaires des groupes réductifs finis(2016), ANR-18-CE40-0024,CATORE,CATEGORIFICATIONS EN TOPOLOGIE ET EN THEORIE DES REPRESENTATIONS(2018) |
| Rok vydání: | 2021 |
| Předmět: |
Finite group
Algebra and Number Theory Group (mathematics) 010102 general mathematics Group Theory (math.GR) Kummer surface Automorphism 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] K3 surface Combinatorics Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics Order (group theory) Mathieu group [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 010307 mathematical physics Geometry and Topology 0101 mathematics Algebraic Geometry (math.AG) Mathematics - Group Theory Symplectic geometry Mathematics |
| Zdroj: | Annales de l'Institut Fourier Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2021, 71 (2), pp.711-730. ⟨10.5802/aif.3411⟩ |
| ISSN: | 1777-5310 0373-0956 |
| DOI: | 10.5802/aif.3411 |
| Popis: | 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. 15 pages |
| Databáze: | OpenAIRE |
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