On the closed image of a rational map and the implicitization problem
| dc.creator | Buse, Laurent | |
| dc.creator | Jouanolou, Jean-Pierre | |
| dc.date | 2002-10-07 | |
| dc.date | 2003-02-11 | |
| dc.date.accessioned | 2026-07-07T04:51:41Z | |
| dc.date.available | 2026-07-07T04:51:41Z | |
| dc.description | In this paper, we investigate some topics around the closed image $S$ of a rational map $λ$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image in case $λ$ is generically finite and $f_1,...,f_n$ define isolated base points in $\Proj(A)$. We then relate the definition ideal of $S$ to the symmetric and the Rees algebras of the ideal $I=(f_1,...,f_n) \subset A$, and prove some new acyclicity criteria for the associated approximation complexes. Finally, we use these results to obtain the implicit equation of $S$ in case $S$ is a hypersurface, $\Proj(A)=\PP^{n-2}_k$ with $k$ a field, and base points are either absent or local complete intersection isolated points. | |
| dc.description | 43 pages, revised version. To appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0210096 | |
| dc.identifier | http://arxiv.org/abs/math/0210096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65199 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14Qxx; 13D02 | |
| dc.title | On the closed image of a rational map and the implicitization problem | |
| dc.type | text |