2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65521Consider 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 pagesAlgebraic GeometryCommutative Algebra14L30; 14M05; 14M15; 14N15text