Rigid Schubert varieties in compact Hermitian symmetric spaces

2011/02/09 by Colleen Robles, Robles, C., The, D. · 2 citations
Mathematics · #14M15 #58A15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1102.1966

openalex publication_date 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces

Cited by

• Realization of Cohomology Classes in Grassmannians
• Realizations of homology classes and projection areas

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