Singularities in the Ekedahl–Oort stratification

We study the Ekedahl–Oort stratification on the special fiber of an abelian type Shimura variety at a prime of good reduction. Originally defined by Oort in the Siegel case via isomorphism classes of p-torsion, this stratification was later extended using the language of G-zips. While the geometry of individual strata is well understood, much less is known about their closures. In this talk, I will present joint work with Lorenzo La Porta and Jean-Stefan Koskivirta giving criteria for normality and Cohen–Macaulayness of unions of EO strata. As applications, we describe the smooth locus of EO strata closures for orthogonal (type Bn) Shimura varieties and obtain general existence results for reduced Hasse invariants.