# Normalization of closed Ekedahl-Oort strata

## TL;DR

This paper uses partial flag space theory to explicitly determine the normalization of Zariski closures of Ekedahl-Oort strata in Shimura varieties of Hodge-type, linking group theory with algebraic geometry.

## Contribution

It introduces a group-theoretical approach to normalize closures of Ekedahl-Oort strata, extending previous theories of partial flag spaces.

## Key findings

- Explicit description of the normalization of strata closures
- Connection between partial flag spaces and Shimura varieties
- Generalization of canonical filtration for truncated Barsotti-Tate groups

## Abstract

We apply our theory of partial flag spaces developed in previous articles to study a group-theoretical generalization of the canonical filtration of a truncated Barsotti-Tate group of level 1. As an application, we determine explicitly the normalization of the Zariski closures of Ekedahl-Oort strata of Shimura varieties of Hodge-type as certain closed coarse strata in the associated partial flag spaces.