%0 Journal Article
%T Rigid Schubert varieties in compact Hermitian symmetric spaces
%A C. Robles
%A D. The
%J Mathematics
%D 2011
%I arXiv
%X Given a singular Schubert variety Z in a compact Hermitian symmetric space it is a longstanding question to determine when Z is homologous to a smooth variety Y. We identify those Schubert varieties for which there exist first-order obstructions to the existence of Y. This extends (independent) work of M. Walters, R. Bryant and J. Hong. Key tools include: (i) a new characterization of Schubert varieties that generalizes the well known description of the smooth Schubert varieties by connected sub-diagrams of a Dynkin diagram; and (ii) an algebraic Laplacian (a la Kostant), which is used to analyze the Lie algebra cohomology group associated to the problem.
%U http://arxiv.org/abs/1102.1966v1