Rigid Schubert varieties in compact Hermitian symmetric spaces
Differential Geometry
2011-02-10 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1102.1966,
title = {Rigid Schubert varieties in compact Hermitian symmetric spaces},
author = {C. Robles and D. The},
journal= {arXiv preprint arXiv:1102.1966},
year = {2011}
}
Comments
52 pages