The implicitization problem for $ϕ: P^n --> (P^1)^{n+1}$
| dc.creator | Botbol, Nicolas | |
| dc.date | 2008-03-05 | |
| dc.date | 2009-03-12 | |
| dc.date.accessioned | 2026-07-07T12:51:05Z | |
| dc.date.available | 2026-07-07T12:51:05Z | |
| dc.description | We develop in this paper some methods for studying the implicitization problem for a rational map $ϕ: \mathbb{P}^n \to (\mathbb{P}^1)^{n+1}$ defining a hypersurface in $(\mathbb{P}^1)^{n+1}$, based on computing the determinant of a graded strand of a Koszul complex. We show that the classical study of Macaulay Resultants and Koszul complexes coincides, in this case, with the approach of approximation complexes and we study and give a geometric interpretation for the acyclicity conditions. Under suitable hypotheses, these techniques enable us to obtain the implicit equation, up to a power, and up to some other extra factor. We give algebraic and geometric conditions for determining when the computed equation defines the scheme theoretic image of $ϕ$, and, what are the extra varieties that appear. We also give some applications to the problem of computing sparse discriminants. | |
| dc.description | 17 pages, revised version. To appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/0803.0573 | |
| dc.identifier | http://arxiv.org/abs/0803.0573 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222884 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.title | The implicitization problem for $ϕ: P^n --> (P^1)^{n+1}$ | |
| dc.type | text |