Fat Points in P^1 x P^1 and their Hilbert Functions
| dc.creator | Guardo, Elena | |
| dc.creator | Van Tuyl, Adam | |
| dc.date | 2002-03-07 | |
| dc.date | 2002-11-04 | |
| dc.date.accessioned | 2026-07-07T04:46:54Z | |
| dc.date.available | 2026-07-07T04:46:54Z | |
| dc.description | We study the Hilbert functions of fat points in P^1 x P^1. If Z is an arbitrary fat point subscheme of P^1 x P^1, then it can be shown that for every i and j the values of the Hilbert function H_Z(l,j) and H_Z(i,l) eventually become constant for l >> 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in P^1 x P^1. This enables us to compute all but a finite number values of H_Z without using the coordinates of points. We also characterize the ACM fat points schemes using our description of the eventual behaviour. In fact, in the case that Z is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function. | |
| dc.description | 23 Pages. Revised version to appear in Can. J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0203071 | |
| dc.identifier | http://arxiv.org/abs/math/0203071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63516 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D40; 14A15 | |
| dc.title | Fat Points in P^1 x P^1 and their Hilbert Functions | |
| dc.type | text |