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arXiv · 1102.1966

Rigid Schubert varieties in compact Hermitian symmetric spaces

C. Robles·D. The
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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.

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C. Robles, D. The. 2011-02-09. Rigid Schubert varieties in compact Hermitian symmetric spaces. https://arxiv.org/abs/1102.1966

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