Singular loci of cominuscule Schubert varieties

Details Singular loci of cominuscule Schubert varieties Singular loci of cominuscule Schubert varieties

2012-03-01

arxiv.org/abs/1203.0324v1

Mathematics

Algebraic Geometry

Two tables for the exceptional E6 and E7

Scientific paper

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 in X in terms of representation theoretic data. The result is based on a recent characterization of the Schubert varieties by an non-negative integer A and a marked Dynkin diagram. Corollaries include: (1) the variety is smooth if and only if A=0; (2) if G of Type ADE, then the singular locus occurs in codimension at least three.

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