Singularities of restriction varieties in OG(k, n)

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.

KEYWORDS:

• Orthogonal Grassmannians
• resolution of singularities
• singular locus

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14M15
• 14E15
• 32M10

Acknowledgements

I would like to thank İzzet Coşkun for his support and advice. I would also like to thank John Christian Ottem for helpful discussions.