Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908597845229568 |
|---|---|
| author | Chau, Trung Das, Kanoy Kumar Roy, Amit Saha, Kamalesh |
| author_facet | Chau, Trung Das, Kanoy Kumar Roy, Amit Saha, Kamalesh |
| contents | We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employing the Tor-vanishing criteria for mixed sums of ideals, we establish sharp lower bounds for their Castelnuovo-Mumford regularity in terms of what we call the admissible set of the associated hypergraph. As an application, we derive the first general combinatorial lower bound for the regularity of squarefree symbolic powers of monomial ideals. In the setting of edge ideals, by exploiting the special combinatorial structures of block graphs and Cohen-Macaulay chordal graphs, we show that this bound turns into an exact formula for all squarefree symbolic powers of block graphs, as well as for the second squarefree symbolic powers of edge ideals of Cohen-Macaulay chordal graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Admissible set and squarefree-power-like function with applications to squarefree symbolic powers Chau, Trung Das, Kanoy Kumar Roy, Amit Saha, Kamalesh Commutative Algebra Combinatorics 13D02, 05E40, 13F55, 05C70 We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employing the Tor-vanishing criteria for mixed sums of ideals, we establish sharp lower bounds for their Castelnuovo-Mumford regularity in terms of what we call the admissible set of the associated hypergraph. As an application, we derive the first general combinatorial lower bound for the regularity of squarefree symbolic powers of monomial ideals. In the setting of edge ideals, by exploiting the special combinatorial structures of block graphs and Cohen-Macaulay chordal graphs, we show that this bound turns into an exact formula for all squarefree symbolic powers of block graphs, as well as for the second squarefree symbolic powers of edge ideals of Cohen-Macaulay chordal graphs. |
| title | Admissible set and squarefree-power-like function with applications to squarefree symbolic powers |
| topic | Commutative Algebra Combinatorics 13D02, 05E40, 13F55, 05C70 |
| url | https://arxiv.org/abs/2510.01366 |