Integrally closed and componentwise linear ideals
| dc.creator | Conca, Aldo | |
| dc.creator | De Negri, Emanuela | |
| dc.creator | Rossi, Maria Evelina | |
| dc.date | 2008-01-22 | |
| dc.date | 2009-04-07 | |
| dc.date.accessioned | 2026-07-07T13:00:58Z | |
| dc.date.available | 2026-07-07T13:00:58Z | |
| dc.description | In two dimensional regular local rings integrally closed ideals have a unique factorization property and have a Cohen-Macaulay associated graded ring. In higher dimension these properties do not hold for general integrally closed ideals and the goal of the paper is to identify a subclass of integrally closed ideals for which they do. We restrict our attention to 0-dimensional homogeneous ideals in polynomial rings $R$ of arbitrary dimension and identify a class of integrally closed ideals, the Goto-class $\G^*$, that is closed under product and that has a suitable unique factorization property. Ideals in $\G^*$ have a Cohen-Macaulay associated graded ring if either they are monomial or $\dim R\leq 3$. Our approach is based on the study of the relationship between the notions of integrally closed, contracted, full and componentwise linear ideals. | |
| dc.description | revised version, references added, to appear in Math. Z | |
| dc.identifier | https://arxiv.org/abs/0801.3373 | |
| dc.identifier | http://arxiv.org/abs/0801.3373 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226012 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13B22; 13D02 | |
| dc.title | Integrally closed and componentwise linear ideals | |
| dc.type | text |