Ekedahl-Oort types of stable curves

Abstract

We discuss an intrinsic definition of Ekedahl-Oort types for stable curves via Moonen's Hasse-Witt triples, previously used for smooth curves. We show that this leads to an equivalent definition to the classical one for the Ekedahl-Oort types of generalized Jacobians as semi-abelian varieties. This approach enables us to compute bounds on the dimensions of many new Ekedahl-Oort loci of curves and to generalize results on the dimensions of the p-rank and a-number loci.