Singular Loci of Restriction Varieties

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 orthogonal Schubert varieties are examples of restriction varieties. In this thesis, we describe a resolution of singularities for restriction varieties in OG(k, n). We study the relationship between the exceptional locus of the resolution and the singularities of a restriction variety. Our study results in a partial description of the singular locus of a restriction variety in terms of the components of the exceptional locus of the resolution of singularities.