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arXiv · 1912.04477

Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity

Jenna Rajchgot·Yi Ren·Colleen Robichaux·Avery St. Dizier·Anna Weigandt
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Abstract

We give an explicit formula for the degree of the Grothendieck polynomial of a Grassmannian permutation and a closely related formula for the Castelnuovo-Mumford regularity of the Schubert determinantal ideal of a Grassmannian permutation. We then provide a counterexample to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri on a formula for regularities of standard open patches of particular Grassmannian Schubert varieties and show that our work gives rise to an alternate explicit formula in these cases. We end with a new conjecture on the regularities of standard open patches of arbitrary Grassmannian Schubert varieties.

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Jenna Rajchgot, Yi Ren, Colleen Robichaux, Avery St. Dizier, Anna Weigandt. 2019-12-10. Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity. https://arxiv.org/abs/1912.04477

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