# Following Schubert varieties under Feigin's degeneration of the flag variety

@article{Bossinger2018FollowingSV, title={Following Schubert varieties under Feigin's degeneration of the flag variety}, author={Lara Bossinger and M. Lanini}, journal={arXiv: Representation Theory}, year={2018} }

We describe the effect of Feigin's flat degeneration of the type $\textrm{A}$ flag variety on its Schubert varieties. In particular, we study when they stay irreducible and in several cases we are able to encode reducibility of the degenerations in terms of symmetric group combinatorics. As a side result, we obtain an identification of some Schubert varieties with Richardson varieties in higher rank partial flag varieties.

#### 3 Citations

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We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed a… Expand

Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties

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We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matching fields in the… Expand

Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian

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Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassmannians by studying… Expand

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