2019/10/14 by Bonnafé, Cédric, Sarti, Alessandra
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1910.05955
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× 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.