On the defining ideal of a set of points in multi-projective space
| dc.creator | Van Tuyl, Adam | |
| dc.date | 2004-09-03 | |
| dc.date.accessioned | 2026-07-07T05:11:47Z | |
| dc.date.available | 2026-07-07T05:11:47Z | |
| dc.description | We investigate the defining ideal of a set of points X in multi-projective space with a special emphasis on the case that X is in generic position, that is, X has the maximal Hilbert function. When X is in generic position, we determine the degrees of the generators of the associated ideal I_X. Letting ν(I_X) denote the minimal number of generators of I_X, we use this description of the degrees to construct a function v(s;n_1,...,n_k) with the property that ν(\Ix) >= v(s;n_1,...,n_k) always holds for s points in generic position in P^{n_1} x ... x P^{n_k}. When k=1, v(s;n_1) equals the expected value for ν(I_X) as predicted by the Ideal Generation Conjecture. If k >= 2, we show that there are cases with ν(\Ix) > v(s;n_1,...,n_k). However, computational evidence suggests that in many cases ν(\Ix) = v(s;n_1,...,n_k). | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409056 | |
| dc.identifier | http://arxiv.org/abs/math/0409056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72363 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D02, 13D40, 14A05 | |
| dc.title | On the defining ideal of a set of points in multi-projective space | |
| dc.type | text |