Singular loci of cominuscule Schubert varieties

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Robles, C

Published Date

  • April 1, 2014

Published In

Volume / Issue

  • 218 / 4

Start / End Page

  • 745 - 759

International Standard Serial Number (ISSN)

  • 0022-4049

Digital Object Identifier (DOI)

  • 10.1016/j.jpaa.2013.08.014

Citation Source

  • Scopus