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Rigidity of singular Schubert varieties in \(\text{Gr}(m,n)\). (English) Zbl 1137.14311

Summary: Let \(a=(p_1^{q_1},\dots, p_r^{q_r})\) be a partition and \(a'=({p_1'}^{q_1'}, >\dots , {p_r'}^{q_r'})\) be its conjugate. We will prove that if \(q_i, q_i \geq 2\) for all \(i\), then any irreducible subvariety \(X\) of \(\text{Gr}(m,n)\) whose homology class is an integral multiple of the Schubert class \([\sigma_a]\) of type \(a\) is a Schubert variety of type \(a\).

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14N15 Classical problems, Schubert calculus
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