Dusan Dragutinovic: Supersingular curves of genus 4 in characteristic 2

Abstract

Abstract: In contrast to supersingular abelian varieties, we know little about supersingular curves in general. We aim to show that the locus of supersingular genus-4 curves in characteristic 2 is 3-dimensional. After presenting some known results, techniques, and applications, we prove the result from two points of view. Our first approach involves an analysis of the data of genus-4 curves and abelian fourfolds over \(\mathbb{F}_2\), and the second one uses a more careful study of the geometry of some relevant Ekedahl–Oort loci.