Singular loci of cominuscule Schubert varieties

Let X = G/ P be a cominuscule rational homogeneous variety. Equivalently, X admits the structure of a compact Hermitian symmetric space. I give a uniform description (that is, independent of type) of the irreducible components of the singular locus of a Schubert variety Y⊂ X in terms of representation theoretic data. The result is based on a recent characterization of the Schubert varieties using an integer a≥ 0 and a marked Dynkin diagram. Corollaries include: (1) the variety is smooth if and only if a= 0; (2) if G is of type ADE, then the singular locus occurs in codimension at least 3. © 2013 Elsevier B.V.

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Author Colleen M Robles Mathematics