The automorphism groups of Kummer surfaces in characteristic two and their complex analogues

TL;DR

This paper computes the automorphism groups of certain Kummer surfaces in characteristic two and explores their complex analogues, providing insights into their symmetries and lattice structures.

Contribution

It determines the automorphism groups of Kummer surfaces in characteristic two and compares them with complex K3 surfaces sharing the same Picard lattice.

Findings

Automorphism groups are explicitly calculated for these Kummer surfaces.

The paper identifies similarities and differences with complex K3 surfaces.

It discusses the implications for symmetries in algebraic geometry.

Abstract

We calculate the automorphism group of the Kummer surface associated with a curve of genus 2 or the product of two elliptic curves in characteristic two under the assumption that the Kummer surface is a $K3$ surface. Moreover we discuss the complex $K3$ surfaces with the same Picard lattice as these Kummer surfaces. The paper has two appendices.