Minimal links and a result of Gaeta
| dc.creator | Migliore, Juan | |
| dc.creator | Nagel, Uwe | |
| dc.date | 2008-04-03 | |
| dc.date.accessioned | 2026-07-07T09:30:08Z | |
| dc.date.available | 2026-07-07T09:30:08Z | |
| dc.description | If $V$ is an equidimensional codimension $c$ subscheme of an $n$-dimensional projective space, and $V$ is linked to $V'$ by a complete intersection $X$, then we say that $V$ is {\em minimally linked} to $V'$ if $X$ is a codimension $c$ complete intersection of smallest degree containing $V$. Gaeta showed that if $V$ is any arithmetically Cohen-Macaulay (ACM) subscheme of codimension two then there is a finite sequence of minimal links beginning with $V$ and arriving at a complete intersection. We extend this work in the following ways: 1) In the codimension 2 non-ACM case, we show that for any $n \geq 3$ there are examples of subschemes that are not minimal in their even liaison class, and cannot be minimally linked in any number of steps to a minimal subscheme. 2) Nevertheless, there are examples of non-ACM liaison classes of curves in projective 3-space where all elements are minimally linked in a finite number of steps to a minimal curve. 3) Extending previous work of the authors with Huneke and Ulrich (about the licci case), we show that also in the non-ACM case in any higher codimension there are non-minimal subschemes that are not minimally linked to a minimal subscheme in the even liaison class. 4) J. Watanabe had shown many years ago that codimension 3 graded Gorenstein ideals of any dimension are licci. Here we show that any such ideal is minimally linked in a finite number of steps to a complete intersection, and that it admits a sequence of strictly decreasing CI-biliaisons down to a complete intersection, extending work of Hartshorne, Sabadini and Schlesinger. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0804.0590 | |
| dc.identifier | http://arxiv.org/abs/0804.0590 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158034 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14M06; 13C40; 14M07; 14F05; 13D02 | |
| dc.title | Minimal links and a result of Gaeta | |
| dc.type | text |