On Kummer type construction of supersingular K3 surfaces in characteristic 2

TL;DR

This paper demonstrates that all supersingular K3 surfaces in characteristic 2 with low Artin invariant can be constructed using Schroeer’s Kummer type method, expanding understanding of their structure.

Contribution

It establishes a complete construction method for certain supersingular K3 surfaces in characteristic 2, linking them to Kummer type constructions.

Findings

All supersingular K3 surfaces with Artin invariant ≤ 2 are obtainable via Schroeer’s Kummer construction.

Provides a classification framework for supersingular K3 surfaces in characteristic 2.

Enhances understanding of the geometric structure of supersingular K3 surfaces.

Abstract

We show that every supersingular K3 surface in characteristic 2 with Artin invariant less than or equal to 2 is obtained by the Kummer type construction of Schroeer.