Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915779750920192 |
|---|---|
| author | Berghofer, Emily Nicklasson, Lisa Thompson, Peder Westerbäck, Thomas |
| author_facet | Berghofer, Emily Nicklasson, Lisa Thompson, Peder Westerbäck, Thomas |
| contents | Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gröbner basis implies the existence of a Koszul filtration for toric algebras equipped with the degree reverse lexicographic term order and for algebras defined by binomial edge ideals. We also resolve a conjecture of Ene, Herzog, and Hibi by constructing an example where this implication fails. These results are underpinned by algorithms we develop for constructing Koszul filtrations. We also demonstrate the utility of these algorithms on the pinched Veronese algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras Berghofer, Emily Nicklasson, Lisa Thompson, Peder Westerbäck, Thomas Commutative Algebra Symbolic Computation Combinatorics Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gröbner basis implies the existence of a Koszul filtration for toric algebras equipped with the degree reverse lexicographic term order and for algebras defined by binomial edge ideals. We also resolve a conjecture of Ene, Herzog, and Hibi by constructing an example where this implication fails. These results are underpinned by algorithms we develop for constructing Koszul filtrations. We also demonstrate the utility of these algorithms on the pinched Veronese algebra. |
| title | Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras |
| topic | Commutative Algebra Symbolic Computation Combinatorics |
| url | https://arxiv.org/abs/2602.06490 |