Classification of K3-surfaces with involution and maximal symplectic symmetry

TL;DR

This paper classifies K3-surfaces with maximal symplectic symmetry, showing they can be constructed as double covers of Del Pezzo surfaces, and explores their involutions and symmetries.

Contribution

It provides a complete classification of K3-surfaces with maximal symplectic symmetry and describes their construction via double covers of Del Pezzo surfaces.

Findings

Actions of large finite groups are realized via double covers of Del Pezzo surfaces.

Complete classification of K3-surfaces with maximal symplectic symmetry.

Analysis of antisymplectic involutions compatible with symplectic actions.

Abstract

K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. In this situation actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo surfaces. A complete classification of K3-surfaces with maximal symplectic symmetry is obtained.