Un théorème de Rao pour les familles de courbes gauches
| dc.creator | Hartshorne, Robin | |
| dc.creator | Martin-Deschamps, Mireille | |
| dc.creator | Perrin, Daniel | |
| dc.date | 1997-10-15 | |
| dc.date.accessioned | 2026-07-07T01:51:12Z | |
| dc.date.available | 2026-07-07T01:51:12Z | |
| dc.description | The aim of this paper is to prove a generalization of a theorem of Rao for families of space curves, which caracterizes the biliaison classes of curves. First we introduce the concept of pseudo-isomorphism of coherent sheaves, which generalizes the concept of stable isomorphism. An N-type resolution for a family of curves $C$ over the local ring $A$, defined by an ideal $J$, is an exact sequence $0\to P\to N\to J\to 0$ where $N$ is a locally free sheaf on $P^3_A$ and $P$ is a direct sum of invertible sheaves $O_P(-n_i)$. We prove the two following results, when the residual field of $A$ is infinite : 1. Let $C$ and $C'$ be two flat families of space curves over the local ring $A$. Then $C$ and $C'$ are in the same biliaison class if and only if their ideals $J$ and $J'$ are pseudo-isomorphic, up to a shift. 2. Let $C$ and $C'$ be two flat families of space curves over the local ring $A$, with N-type resolutions, involving sheaves $N$ and $N'$. Then $C$ and $C'$ are in the same biliaison class if and only if $N$ and $N'$ are pseudo-isomorphic, up to a shift. | |
| dc.description | 22 pages, TeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9710017 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9710017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/234 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Un théorème de Rao pour les familles de courbes gauches | |
| dc.type | text |