On tangent cones to Schubert varieties in type $E$

Mikhail V. Ignatyev; Aleksandr A. Shevchenko

On tangent cones to Schubert varieties in type $E$

Algebraic Geometry 2020-07-09 v1

Authors: Mikhail V. Ignatyev , Aleksandr A. Shevchenko

Abstract

We consider tangent cones to Schubert subvarieties of the flag variety $G/B$ , where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of type $E_6$ , $E_7$ or $E_8$ . We prove that if $w_1$ and $w_2$ form a good pair of involutions in the Weyl group $W$ of $G$ then the tangent cones $C_{w_1}$ and $C_{w_2}$ to the corresponding Schubert subvarieties of $G/B$ do not coincide as subschemes of the tangent space to $G/B$ at the neutral point.

Keywords

flag varieties

Cite

@article{arxiv.2007.04110,
  title  = {On tangent cones to Schubert varieties in type $E$},
  author = {Mikhail V. Ignatyev and Aleksandr A. Shevchenko},
  journal= {arXiv preprint arXiv:2007.04110},
  year   = {2020}
}

Comments

15 pages. arXiv admin note: substantial text overlap with arXiv:1410.4025, arXiv:1310.3166, arXiv:1210.5740

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