# Toric degenerations of flag varieties from matching field tableaux

@article{Clarke2019ToricDO, title={Toric degenerations of flag varieties from matching field tableaux}, author={Oliver Clarke and Fatemeh Mohammadi}, journal={arXiv: Commutative Algebra}, year={2019} }

We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Plucker algebras. We show that each such family of tableaux leads to a toric ideal, that can be realized as initial of the Plucker ideal, hence a toric degeneration for the flag variety.

## 6 Citations

Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2021

An analogue of matching field ideals for Schubert varieties inside the flag variety and a complete characterization of toric ideals among them are described to show that block diagonal matching fields give rise to toric degenerations.

Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux

- Mathematics
- 2020

Abstract We study Grobner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed by matching field tableaux in…

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

- Mathematics
- 2020

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…

Standard monomial theory and toric degenerations of Richardson varieties in flag varieties

- Mathematics
- 2021

We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, as it involves…

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

- Mathematics
- 2021

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…

Combinatorial mutations and block diagonal polytopes

- Mathematics
- 2020

Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various families of varieties.…

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Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux

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An analogue of matching field ideals for Schubert varieties inside the flag variety and a complete characterization of toric ideals among them are described to show that block diagonal matching fields give rise to toric degenerations.

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Abstract We study Grobner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed by matching field tableaux in…

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

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