Degrees of P-Grothendieck polynomials and regularity of Pfaffian varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913399292559360 |
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| author | Pechenik, Oliver Denis, Matthew St. |
| author_facet | Pechenik, Oliver Denis, Matthew St. |
| contents | We prove a formula for the degrees of Ikeda and Naruse's $P$-Grothendieck polynomials using combinatorics of shifted tableaux. We show this formula can be used in conjunction with results of Hamaker, Marberg, and Pawlowski to obtain an upper bound on the Castelnuovo-Mumford regularity of certain Pfaffian varieties known as vexillary skew-symmetric matrix Schubert varieties. Similar combinatorics additionally yields a new formula for the degree of Grassmannian Grothendieck polynomials and the regularity of Grassmannian matrix Schubert varieties, complementing a 2021 formula of Rajchgot, Ren, Robichaux, St. Dizier, and Weigandt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degrees of P-Grothendieck polynomials and regularity of Pfaffian varieties Pechenik, Oliver Denis, Matthew St. Combinatorics Commutative Algebra Algebraic Geometry 05E05, 05E40, 13C40, 14M15 We prove a formula for the degrees of Ikeda and Naruse's $P$-Grothendieck polynomials using combinatorics of shifted tableaux. We show this formula can be used in conjunction with results of Hamaker, Marberg, and Pawlowski to obtain an upper bound on the Castelnuovo-Mumford regularity of certain Pfaffian varieties known as vexillary skew-symmetric matrix Schubert varieties. Similar combinatorics additionally yields a new formula for the degree of Grassmannian Grothendieck polynomials and the regularity of Grassmannian matrix Schubert varieties, complementing a 2021 formula of Rajchgot, Ren, Robichaux, St. Dizier, and Weigandt. |
| title | Degrees of P-Grothendieck polynomials and regularity of Pfaffian varieties |
| topic | Combinatorics Commutative Algebra Algebraic Geometry 05E05, 05E40, 13C40, 14M15 |
| url | https://arxiv.org/abs/2405.17645 |