posted on 14.05.2012, 00:00by Richard Abdelkerim, Izzet Coskun
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 paper, we describe the spaces of Schubert varieties contained in hyperplane sections of G(2; n). The group PGL(n) acts with nitely many orbits on the dual of the Plucker space P*(V2 V). The orbits are determined by the singular locus of H \G(2; n). For H in each orbit, we describe the spaces of Schubert varieties contained in H \ G(2; n). We also discuss some generalizations to G(k; n).
During the preparation of this article the second author was partially supported by the NSF grant DMS-0737581, the NSF CAREER grant DMS-0950951535, and an Alfred P. Sloan Foundation Fellowship.
NOTICE: this is the author’s version of a work that was accepted for publication in the Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the Journal of Pure and Applied Algebra, Vol 216, Issue 4, Apr 2012 DOI: 10.1016/j.jpaa.2011.08.013