Triades et familles de courbes gauches
| dc.creator | Hartshorne, Robin | |
| dc.creator | Martin-Deschamps, Mireille | |
| dc.creator | Perrin, Daniel | |
| dc.date | 1998-03-24 | |
| dc.date.accessioned | 2026-07-07T05:24:10Z | |
| dc.date.available | 2026-07-07T05:24:10Z | |
| dc.description | Let $A$ be a noetherian ring and $R_A$ be the graded ring $A[X,Y,Z,T]$. In this article we introduce the notion of a triad, which is a generalization to families of curves in ${\bf P}^3_A$ of the notion of Rao module. A triad is a complex of graded $R_A$-modules $(L_1 \to L_0 \to L_{-1})$ with certain finiteness hypotheses on its cohomology modules. A pseudo-isomorphism between two triads is a morphism of complexes which induces an isomorphism on the functors $ h_0 (L\otimes .)$ and a monomorphism on the functors $h_{-1} (L\otimes .)$. One says that two triads are pseudo-isomorphic if they are connected by a chain of pseudo-isomorphisms. We show that to each family of curves is associated a triad, unique up to pseudo-isomorphism, and we show that the map $\{\hbox{families of curves}\}\to \{\hbox{triads}\}$ has almost all the good properties of the map $\{\hbox{curves}\}\to \{\hbox{Rao modules}\}$. In a section of examples, we show how to construct triads and families of curves systematically starting from a graded module and a sub-quotient (that is a submodule of a quotient module), and we apply these results to show the connectedness of $H_{4,0}$. | |
| dc.description | 59 pages, TeX | |
| dc.identifier | https://arxiv.org/abs/math/9803111 | |
| dc.identifier | http://arxiv.org/abs/math/9803111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76736 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Triades et familles de courbes gauches | |
| dc.type | text |