Parameter spaces of Schubert varieties in hyperplane sections of Grassmannians

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 finitely many orbits on the dual of the Plücker space P∗(⋀2V). 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).