The Ideal Generation Problem for Fat Points
| dc.creator | Harbourne, Brian | |
| dc.date | 1997-03-27 | |
| dc.date.accessioned | 2026-07-07T09:07:14Z | |
| dc.date.available | 2026-07-07T09:07:14Z | |
| dc.description | This paper is concerned with determining the number of generators in each degree for minimal sets of homogeneous generators for saturated ideals defining fat point subschemes $Z=m_1p_1+ ... +m_rp_r$ for general sets of points $p_i$ of $P^2$. For thin points (i.e., m_i=1 for all i), a solution is known, in terms of a maximal rank property. Although this property in general fails for fat points, we show it holds in an appropriate asymptotic sense. In the uniform (i.e., $m_1= ... =m_r$) case, we determine all failures of this maximal rank property for $r\le 9$, and we develop evidence for the conjecture that no other failures occur for $r > 9$. | |
| dc.description | PlainTeX, 17 pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9703035 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9703035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150300 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Ideal Generation Problem for Fat Points | |
| dc.type | text |