Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties

We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in previous joint work of the authors with Y. Ren and...

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Bibliographic Details
Published inJournal of algebra Vol. 617; pp. 160 - 191
Main Authors Rajchgot, Jenna, Robichaux, Colleen, Weigandt, Anna
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2023
Subjects
Castelnuovo-Mumford regularity
Grassmannian
Grothendieck polynomial
Ladder determinantal ideal
Matrix Schubert variety
Grassmannian
Ladder determinantal ideal
Castelnuovo-Mumford regularity
Matrix Schubert variety
Grothendieck polynomial
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Summary:We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in previous joint work of the authors with Y. Ren and A. St. Dizier. We apply our formulas to compute Castelnuovo-Mumford regularity of classes of generalized determinantal ideals. In particular, we give combinatorial formulas for the regularities of all one-sided mixed ladder determinantal ideals. We also derive formulas for the regularities of certain Kazhdan-Lusztig ideals, including those coming from open patches of Schubert varieties in Grassmannians. This provides a correction to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri (2015).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.11.001