Selecta Mathematica

, Volume 18, Issue 3, pp 717–777 | Cite as

Rigid Schubert varieties in compact Hermitian symmetric spaces

Article

Abstract

Given a singular Schubert variety Xw in a compact Hermitian symmetric space X, it is a long-standing question to determine when Xw 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 (à la Kostant), which is used to analyze the Lie algebra cohomology group associated with the problem.

Keywords

Schubert variety Compact Hermitian symmetric space Lie algebra cohomology 

Mathematics Subject Classification (2000)

14M15 58A15 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentTAMUCollege StationUSA

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