Multiplicity-free subvarieties of flag varieties

Abstract

Consider a flag variety $Fl$ over an algebraically closed field, and a subvariety $V$ whose cycle class is a multiplicity-free sum of Schubert cycles. We show that $V$ is arithmetically normal and Cohen-Macaulay, in the projective embedding given by any ample invertible sheaf on $Fl$.

LaTeX, 13 pages