An unusual family of supersingular curves of genus five

2025/07/04 by Dragutinović, Dušan
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.03519

Abstract

We construct a family of smooth supersingular curves of genus 5 in characteristic 2 with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus 5, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-2 curve. We also provide an explicit parametrization of this family.

Citations

• Supersingular Ekedahl-Oort strata and Oort's conjecture
• Oort's conjecture and automorphisms of supersingular curves of genus four
• Supersingular curves of genus four in characteristic two
• Computing binary curves of genus five
• A census of all genus 4 curves over the field with 2 elements
• Fully maximal and fully minimal abelian varieties
• Hyperelliptic curves in characteristic 2
• On the Existence of Supersingular Curves of Given Genus

Related

• Producing supersingular curves of genus five
• Families of supersingular curves in characteristic 2
• On the Existence of Supersingular Curves of Given Genus
• Superspecial genus-4 double covers of elliptic curves
• Classifying families of superelliptic curves