Hilbert functions of d-regular ideals
| dc.creator | Murai, Satoshi | |
| dc.date | 2006-11-01 | |
| dc.date | 2007-06-26 | |
| dc.date.accessioned | 2026-07-07T08:12:20Z | |
| dc.date.available | 2026-07-07T08:12:20Z | |
| dc.description | In the present paper, we characterize all possible Hilbert functions of graded ideals in a polynomial ring whose regularity is smaller than or equal to $d$, where $d$ is a positive integer. In addition, we prove the following result which is a generalization of Bigatti, Hulett and Pardue's result: Let $p \geq 0$ and $d>0$ be integers. If the base field is a field of characteristic 0 and there is a graded ideal $I$ whose projective dimension $\mathrm{proj\ dim}(I)$ is smaller than or equal to $p$ and whose regularity $\mathrm{reg}(I)$ is smaller than or equal to $d$, then there exists a monomial ideal $L$ having the maximal graded Betti numbers among graded ideals $J$ which have the same Hilbert function as $I$ and which satisfy $\mathrm{proj dim}(J) \leq p$ and $\mathrm{reg}(J) \leq d$. We also prove the same fact for squarefree monomial ideals. The main methods for proofs are generic initial ideals and combinatorics on strongly stable ideals. | |
| dc.description | 33 pages, minor changes, to appear in J. Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0611020 | |
| dc.identifier | http://arxiv.org/abs/math/0611020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132419 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13D40;13D02,13F55 | |
| dc.title | Hilbert functions of d-regular ideals | |
| dc.type | text |