Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
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_ | 1866918516356022272 |
|---|---|
| author | Cooper, Susan M. Khoury, Sabine El Faridi, Sara Morey, Susan Sega, Liana M. Spiroff, Sandra |
| author_facet | Cooper, Susan M. Khoury, Sabine El Faridi, Sara Morey, Susan Sega, Liana M. Spiroff, Sandra |
| contents | Using divisibility relations between the generators of a square-free monomial ideal $I$, we describe divisibility relations between the generators of the second power $I^2$. We then employ discrete Morse theory to produce a cellular free resolution of $I^2$ which is minimal for specific ideals that are extremal with respect to a given divisibility relation. In particular, we provide sharp bounds on the projective dimension of $I^2$ when the generators of $I$ satisfy at least one divisibility relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22280 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cellular resolutions of second powers of square-free monomial ideals with divisibility relations Cooper, Susan M. Khoury, Sabine El Faridi, Sara Morey, Susan Sega, Liana M. Spiroff, Sandra Commutative Algebra Combinatorics 13D02, 13F55, 05E40 Using divisibility relations between the generators of a square-free monomial ideal $I$, we describe divisibility relations between the generators of the second power $I^2$. We then employ discrete Morse theory to produce a cellular free resolution of $I^2$ which is minimal for specific ideals that are extremal with respect to a given divisibility relation. In particular, we provide sharp bounds on the projective dimension of $I^2$ when the generators of $I$ satisfy at least one divisibility relation. |
| title | Cellular resolutions of second powers of square-free monomial ideals with divisibility relations |
| topic | Commutative Algebra Combinatorics 13D02, 13F55, 05E40 |
| url | https://arxiv.org/abs/2605.22280 |