Geometry of the Dual Grassmannian
thesisposted on 20.10.2011 by Richard Abdelkerim
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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).