# Singularities of Restriction Varieties in $OG(k, n)$

## TL;DR

This paper introduces a resolution of singularities for restriction varieties in orthogonal Grassmannians and characterizes their singular locus through the exceptional components of this resolution.

## Contribution

It provides the first explicit resolution of singularities for restriction varieties in $OG(k, n)$ and describes their singular locus in terms of the exceptional components.

## Key findings

- Resolution of singularities constructed for restriction varieties
- Description of singular locus via exceptional components
- Applicable to Schubert varieties of Type B and D

## Abstract

Restriction varieties in the orthogonal Grassmannian are subvarieties of $OG(k, n)$ defined by rank conditions given by a flag that is not necessarily isotropic with respect to the relevant symmetric bilinear form. In particular, Schubert varieties of Type B and D are examples of restriction varieties. In this paper, we introduce a resolution of singularities for restriction varieties in $OG(k, n)$, and give a description of their singular locus by studying components of the exceptional locus of the resolution.