Intersections of the automorphism and the Ekedahl-Oort strata in M₂

2025/07/09 by Alvaro Gonzalez-Hernandez, Gonzalez-Hernandez, Alvaro
Mathematics · #11G10 #11G15 #11G20 #14G17 #14K10 (Primary) #14K15 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.07278

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the intersections between the automorphism strata and the pullback by the Torelli map of the Ekedahl-Oort strata inside the moduli space of genus two curves. We first describe explicitly which possible automorphism groups a genus two curve can have over a field of positive characteristic, and parametrise the families of curves with a prescribed automorphism group. Then, we describe an algorithm to compute the strata of genus two curves whose Jacobian variety has a fixed Ekedahl-Oort type. Finally, we compute the dimension and number of irreducible components of the intersections between the strata.

Citations

• Constructing all Genus 2 Curves with Supersingular Jacobian
• On Büchi's K3 surface
• Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties
• Curves of genus 2 with group of automorphisms isomorphic to D₈ or D₁2
• Cycles on the Moduli Space of Abelian Varieties

Related

• Ekedahl-Oort strata of curves of genus four in characteristic three
• Ekedahl-Oort strata on the moduli space of curves of genus four
• Computing discrete invariants of varieties in positive characteristic. I. Ekedahl-Oort types of curves
• Field of moduli and field of definition for curves of genus 2
• Curves of genus two over fields of even characteristic