The depth of an ideal with a given Hilbert function
| dc.creator | Murai, Satoshi | |
| dc.creator | Hibi, Takayuki | |
| dc.date | 2006-08-08 | |
| dc.date | 2008-12-01 | |
| dc.date.accessioned | 2026-07-07T12:07:19Z | |
| dc.date.available | 2026-07-07T12:07:19Z | |
| dc.description | Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $°x_i = 1$. Let $I$ be a homogeneous ideal of $A$ with $I \ne A$ and $H_{A/I}$ the Hilbert function of the quotient algebra $A / I$. Given a numerical function $H : \mathbb{N} \to \mathbb{N}$ satisfying $H=H_{A/I}$ for some homogeneous ideal $I$ of $A$, we write $\mathcal{A}_H$ for the set of those integers $0 \leq r \leq n$ such that there exists a homogeneous ideal $I$ of $A$ with $H_{A/I} = H$ and with $\depth A / I = r$. It will be proved that one has either $\mathcal{A}_H = \{0, 1, ..., b \}$ for some $0 \leq b \leq n$ or $|\mathcal{A}_H| = 1$. | |
| dc.description | 6 pages, change the numbering of theorems | |
| dc.identifier | https://arxiv.org/abs/math/0608188 | |
| dc.identifier | http://arxiv.org/abs/math/0608188 | |
| dc.identifier | Proc. Amer. Math. Soc. 136 (2008), 1533--1538 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208931 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13C15; 13D40 | |
| dc.title | The depth of an ideal with a given Hilbert function | |
| dc.type | text |