Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1

TL;DR

This paper classifies genus 1 fibrations on a specific supersingular K3 surface in characteristic 2, revealing their structure through lattice theory and geometric configurations.

Contribution

It provides a complete classification of genus 1 fibrations on the supersingular K3 surface with Artin invariant 1 using lattice bijections and geometric analysis.

Findings

Classified all genus 1 fibrations on the surface

Established isomorphisms between different models of the surface

Analyzed a configuration of (-2)-curves related to projective plane incidence

Abstract

The supersingular K3 surface X in characteristic 2 with Artin invariant 1 admits several genus 1 fibrations (elliptic and quasi-elliptic). We use a bijection between fibrations and definite even lattices of rank 20 and discriminant 4 to classify the fibrations, and exhibit isomorphisms between the resulting models of X. We also study a configuration of (-2)-curves on X related to the incidence graph of points and lines of IP^2(IF_4).