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

Abstract

Let a = (pq11, . . ., pqrr) be a partition and a′ = (pq11, . . ., pqrr) 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. © 2005 Applied Probability Trust.