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March 2011 Rigid and non-smoothable Schubert classes
Izzet Coskun
J. Differential Geom. 87(3): 493-514 (March 2011). DOI: 10.4310/jdg/1312998233


A Schubert class $\sigma_\lambda$ in the Grassmannian $G(k, n)$ is rigid if the only proper subvarieties representing that class are Schubert varieties $\Sigma_\lambda$. We prove that a Schubert class $\sigma_\lambda$ is rigid if and only if it is defined by a partition $\lambda$ satisfying a simple numerical criterion. If $\lambda$ fails this criterion, then there is a corresponding hyperplane class in another Grassmannian $G(k', n')$ such that the deformations of the hyperplane in $G(k', n')$ yield non-trivial deformations of the Schubert variety $\Sigma_\lambda$. We also prove that, if a partition λ contains a sub-partition defining a rigid and singular Schubert class in another Grassmannian $G(k', n')$, then there does not exist a smooth subvariety of $G(k, n)$ representing $\sigma_\lambda$.


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Izzet Coskun. "Rigid and non-smoothable Schubert classes." J. Differential Geom. 87 (3) 493 - 514, March 2011.


Published: March 2011
First available in Project Euclid: 10 August 2011

zbMATH: 1232.14032
MathSciNet: MR2819546
Digital Object Identifier: 10.4310/jdg/1312998233

Rights: Copyright © 2011 Lehigh University

Vol.87 • No. 3 • March 2011
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