Gorenstein Biliaison and ACM Sheaves
| dc.creator | Casanellas, Marta | |
| dc.creator | Hartshorne, Robin | |
| dc.date | 2003-04-28 | |
| dc.date.accessioned | 2026-07-07T04:57:29Z | |
| dc.date.available | 2026-07-07T04:57:29Z | |
| dc.description | Let $X$ be a normal arithmetically Gorenstein scheme in ${\mathbb P}^n$. We give a criterion for all codimension two ACM subschemes of $X$ to be in the same Gorenstein biliaison class on $X$, in terms of the category of ACM sheaves on $X$. These are sheaves that correspond to the graded maximal Cohen--Macaulay modules on the homogeneous coordinate ring of $X$. Using known results on MCM modules, we are able to determine the Gorenstein biliaison classes of codimension two subschemes of certain varieties, including the nonsingular quadric surface in ${\mathbb P}^3$, and the cone over it in ${\mathbb P}^4$. As an application we obtain a new proof of some theorems of Lesperance about curves in ${\mathbb P}^4$, and answer some questions be raised. | |
| dc.description | Key words and phrases: linkage, liaison, biliaison, Gorenstein scheme, maximal Cohen-Macaulay modules; 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304447 | |
| dc.identifier | http://arxiv.org/abs/math/0304447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67280 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14M06; 13C40; 13C14 | |
| dc.title | Gorenstein Biliaison and ACM Sheaves | |
| dc.type | text |