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

Jaehyun Hong
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Abstract

Let a=(p_1^{q_1}, ..., p_r^{q_r}) be a partition and a'=({p_1'}^{q_1'}, >..., {p_r'}^{q_r'}) be its conjugate. We will prove that if q_i, q_i > 1 for all i, then any irreducible subvariety X of Gr(m,n) whose homology class is an integral multiple of the Schubert class [σ_a] of type a is a Schubert variety of type a.

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Jaehyun Hong. 2004-10-07. Rigidity of singular Schubert varieties in Gr(m,n). https://arxiv.org/abs/math/0410196

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