Ideal transition systems
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908789173649408 |
|---|---|
| author | Marberg, Eric Pawlowski, Brendan |
| author_facet | Marberg, Eric Pawlowski, Brendan |
| contents | We study an inductive method of computing initial ideals and Gröbner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs $(I,J)$ where $I$ is any ideal and $J$ is a monomial ideal contained in the initial ideal of $I$. These containments become a system of equalities if one can establish a particular transition recurrence among the chosen ideals. We describe explicit constructions of such systems in two motivating cases -- namely, for the ideals of matrix Schubert varieties and their skew-symmetric analogues. Despite many formal similarities with these examples, for the symmetric versions of matrix Schubert varieties, it is an open problem to construct the same kind of transition system. We present several conjectures that would follow from such a construction, while also discussing the special obstructions arising in the symmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ideal transition systems Marberg, Eric Pawlowski, Brendan Commutative Algebra Combinatorics We study an inductive method of computing initial ideals and Gröbner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs $(I,J)$ where $I$ is any ideal and $J$ is a monomial ideal contained in the initial ideal of $I$. These containments become a system of equalities if one can establish a particular transition recurrence among the chosen ideals. We describe explicit constructions of such systems in two motivating cases -- namely, for the ideals of matrix Schubert varieties and their skew-symmetric analogues. Despite many formal similarities with these examples, for the symmetric versions of matrix Schubert varieties, it is an open problem to construct the same kind of transition system. We present several conjectures that would follow from such a construction, while also discussing the special obstructions arising in the symmetric case. |
| title | Ideal transition systems |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2412.17320 |