Rigidity of singular Schubert varieties in Gr(m,n)

Abstract

Let a = (pq11, . . . , pqrr) be a partition and a' = (p'1q'1, . . . , p'rq'r) be its conjugate. We will prove that if qi, q'i ≥ 2 for all 1 ≤ i ≤ r, then any irreducible subvariety X of Gr(m, n) whose homology class is an integral multiple of the Schubert class [σa] of type a is a Schubert variety of type a.