Resolutions of ideals of fat points with support in a hyperplane
| dc.creator | Fatabbi, Giuliana | |
| dc.creator | Harbourne, Brian | |
| dc.creator | Lorenzini, Anna | |
| dc.date | 2005-02-19 | |
| dc.date | 2005-07-11 | |
| dc.date.accessioned | 2026-07-07T05:17:11Z | |
| dc.date.available | 2026-07-07T05:17:11Z | |
| dc.description | Our results concern minimal graded free resolutions of fat point ideals for points in a hyperplane. Suppose, for example, that I(m,d) is the ideal defining r given points of multiplicity m in the projective space P^d. Assume that the given points lie in a hyperplane P^{d-1} in P^d, and that the ground field k is algebraically closed of characteristic 0. We give an explicit minimal graded free resolution of I(m,d) in k[P^d] in terms of the minimal graded free resolutions of the ideals I(j,d-1) in k[P^{d-1}] with j < m+1. As a corollary, we give the following formula for the Poincare polynomial P_{m,d} of I(m,d) in terms of the Poincare polynomials P_{j,d-1} of I(j,d-1): P_{m,d} = (1 + XT)(Σ_{0<j\le m} T^{m-j}(P_{j,d-1} - 1)) + 1 + XT^m. | |
| dc.description | 10 pages; to appear in Proc. Amer. Math. Soc.; some expositional changes; added a reference to paper of Geramita, Migliore and Sabourin (math.AC/0411445) | |
| dc.identifier | https://arxiv.org/abs/math/0502418 | |
| dc.identifier | http://arxiv.org/abs/math/0502418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74257 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14Q99; 13D02 | |
| dc.title | Resolutions of ideals of fat points with support in a hyperplane | |
| dc.type | text |