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Singular Loci of Restriction Varieties

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thesis
posted on 19.10.2016 by Riza Seckin Adali
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.

History

Advisor

Coskun, Izzet

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Ein, Lawrence Huizenga, Jack Riedl, Eric Tucker, Kevin

Submitted date

2016-08

Language

en

Issue date

19/10/2016

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