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Rigid Schubert varieties in compact Hermitian symmetric spaces

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Abstract

Given a singular Schubert variety X w in a compact Hermitian symmetric space X, it is a long-standing question to determine when X w 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.

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  1. Mathematics Department, TAMU, Mail-stop 3368, College Station, TX, 77843-3368, USA

    C. Robles & D. The

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  1. C. Robles
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Correspondence to C. Robles.

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C. Robles: Partially supported by NSF-DMS 1006353. D. The: Partially supported by an NSERC Postdoctoral Fellowship.

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Robles, C., The, D. Rigid Schubert varieties in compact Hermitian symmetric spaces. Sel. Math. New Ser. 18, 717–777 (2012). https://doi.org/10.1007/s00029-011-0082-y

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