Rigid and non-smoothable schubert classes

Izzet Coskun University of Illinois at Chicago

Differential Geometry mathscidoc:1609.10214

Journal of Differential Geometry, 87, (3), 493-514, 2011
A Schubert class  in the Grassmannian G(k, n) is rigid if the only proper subvarieties representing that class are Schubert varieties . We prove that a Schubert class  is rigid if and only if it is defined by a partition  satisfying a simple numerical criterion. If  fails this criterion, then there is a corresponding hyperplane class in another Grassmannian G(k0, n0) such that the deformations of the hyperplane in G(k0, n0) yield non-trivial deformations of the Schubert variety . We also prove that, if a partition  contains a sub-partition defining a rigid and singular Schubert class in another Grassmannian G(k0, n0), then there does not exist a smooth subvariety of G(k, n) representing .
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@inproceedings{izzet2011rigid,
  title={RIGID AND NON-SMOOTHABLE SCHUBERT CLASSES},
  author={Izzet Coskun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912071615502746873},
  booktitle={Journal of Differential Geometry},
  volume={87},
  number={3},
  pages={493-514},
  year={2011},
}
Izzet Coskun. RIGID AND NON-SMOOTHABLE SCHUBERT CLASSES. 2011. Vol. 87. In Journal of Differential Geometry. pp.493-514. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160912071615502746873.
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