Linear Systems of Plane Curves with Base Points of Equal Multiplicity
| dc.creator | Ciliberto, C. | |
| dc.creator | Miranda, R. | |
| dc.date | 1998-04-03 | |
| dc.date.accessioned | 2026-07-07T05:24:18Z | |
| dc.date.available | 2026-07-07T05:24:18Z | |
| dc.description | In this article we address the problem of computing the dimension of the space of plane curves of degree $d$ with $n$ general points of multiplicity $m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing a multiple $(-1)$-curve. We reformulate this conjecture by explicitly listing those systems which have unexpected dimension. Then we use a degeneration technique developed in a previous article ("Degenerations of Planar Linear Systems", alg-geom/9702015) to show that the conjecture holds for all $m \leq 12$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/9804018 | |
| dc.identifier | http://arxiv.org/abs/math/9804018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76787 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Linear Systems of Plane Curves with Base Points of Equal Multiplicity | |
| dc.type | text |