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arXiv · 2202.03995

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

Jenna Rajchgot·Colleen Robichaux·Anna Weigandt
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Abstract

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).

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Jenna Rajchgot, Colleen Robichaux, Anna Weigandt. 2022-02-08. Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties. https://arxiv.org/abs/2202.03995

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