Rigidity of smooth Schubert varieties in a rational homogeneous manifold associated to a short root

Abstract

We classify smooth Schubert varieties S0 in a rational homogeneous manifold S associated to a short root, and show that they are rigid in the sense that any subvariety of S having the same homology class as S0 is induced by the action of Aut0(S), unless S0 is linear.

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