Rigid and Non-smoothable Schubert Classes

  title={Rigid and Non-smoothable Schubert Classes},
  author={Izzet Coskun},
A Schubert class in the Grassmannian is rigid if the only proper subvarieties representing that class are Schubert varieties. The hyperplane class σ1 is not rigid because a codimension one Schubert cycle can be deformed to a smooth hyperplane section. In this paper, we show that this phenomenon accounts for the failure of rigidity in Schubert classes. More precisely, we prove that a Schubert class in G(k, n) is not rigid if and only if the partition λ = (λ1, . . . , λk) defining the class has a… CONTINUE READING

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