Ekedahl-Oort strata of curves of genus four in characteristic three

Abstract

We study the induced Ekedahl-Oort stratification on the moduli space ${\mathcal{M}}_4$ of curves of genus $4$ in characteristic $3$. By constructing families of curves with given Ekedahl-Oort type and by computing the dimension of the intersection of the induced Ekedahl-Oort strata and the boundary divisor classes, we show that for certain induced Ekedahl-Oort strata in ${\mathcal{M}}_4$, they have the same codimension in ${\mathcal{M}}_4$ as the corresponding Ekedahl-Oort strata in moduli space ${\mathcal{A}}_4$ of principally polarized abelian varieties of dimension $4$.

13 pages

References in corpus (2)

• The Dieudonné modules and Ekedahl-Oort types of Jacobians of hyperelliptic curves in odd characteristic
• Ekedahl-Oort strata on the moduli space of curves of genus four