Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
arXiv:1904.00981 · doi:10.1016/j.jalgebra.2020.05.017
Abstract
We study the combinatorics of Gröbner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed by tableaux induced by matching fields in the sense of Sturmfels and Zelevinsky. We prove that these ideals are all quadratically generated and they yield a SAGBI basis of the Plücker algebra. This leads to a new family of toric degenerations of Grassmannians. Moreover, we apply our results to construct a family of Gröbner degenerations of Schubert varieties inside Grassmannians. We provide a complete characterization of toric ideals among these degenerations in terms of the combinatorics of matching fields, permutations, and semi-standard tableaux.
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Cited by in corpus (5)
- Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
- Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras
- Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
- Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
- Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs