## Geometry of the Dual Grassmannian

thesis

posted on 20.10.2011 by Richard Abdelkerim#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

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. In this monograph, we describe the spaces of Schubert varieties contained in hyperplane sections of G(2,n). The group PGL(n) acts with finitely many orbits on the dual of the Plucker space P^*(\bigwedge^2 V ). The orbits are determined by the singular locus of a hyperplane section. For H in each orbit, we describe the spaces of Schubert varieties contained in the hyperplane section. We also discuss some generalizations to G(k,n).