Thesis Defense
Richard Abdelkerim
UIC
Geometry of the Dual Grassmannian
Abstract: Linear sections of Grassmannians provide important examples of varieties. The geometry of these linear sections is closely tied to the spaces of Schubert varieties contained in them. We describe the spaces of Schubert varieties contained in hyperplane sections of $G(2,n)$. The group $\mathbb{P} GL(n)$ acts with finitely many orbits on the dual of the Pl\"{u}cker space $\mathbb{P}^*(\bigwedge^2 V )$. The orbits are determined by the singular locus of $H \cap G(2,n)$. For $H$ in each orbit, we describe the spaces of Schubert varieties contained in $H \cap G(2,n)$. We also discuss some generalizations to $G(k,n)$.
Monday March 7, 2011 at 1:00 PM in SEO 1227