Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity Academic Article uri icon

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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.

authors

  • Rajchgot, Jenna
  • Ren, Yi
  • Robichaux, Colleen
  • St. Dizier, Avery
  • Weigandt, Anna

publication date

  • April 1, 2021