Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux
Commutative Algebra
2020-09-08 v1 Combinatorics
Abstract
We study Gr\"obner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tableaux. We describe an analogue of matching field ideals for Schubert varieties inside the flag variety and give a complete characterization of toric ideals among them. We use a combinatorial approach to standard monomial theory to show that block diagonal matching fields give rise to toric degenerations. Our methods and results use the combinatorics of permutations associated to Schubert varieties, matching fields and their corresponding tableaux.
Keywords
Cite
@article{arxiv.2009.03215,
title = {Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux},
author = {Oliver Clarke and Fatemeh Mohammadi},
journal= {arXiv preprint arXiv:2009.03215},
year = {2020}
}