Curves having one place at infinity and linear systems on rational surfaces
| dc.creator | Monserrat, F. | |
| dc.date | 2006-07-26 | |
| dc.date.accessioned | 2026-07-07T07:20:59Z | |
| dc.date.available | 2026-07-07T07:20:59Z | |
| dc.description | Denoting by ${\mathcal L}_d(m_0,m_1,...,m_r)$ the linear system of plane curves passing through $r+1$ generic points $p_0,p_1,...,p_r$ of the projective plane with multiplicity $m_i$ (or larger) at each $p_i$, we prove the Harbourne-Hirschowitz Conjecture for linear systems ${\mathcal L}_d(m_0,m_1,...,m_r)$ determined by a wide family of systems of multiplicities $\bold{m}=(m_i)_{i=0}^r$ and arbitrary degree $d$. Moreover, we provide an algorithm for computing a bound of the regularity of an arbitrary system $\bold{m}$ and we give its exact value when $\bold{m}$ is in the above family. To do that, we prove an $H^1$-vanishing theorem for line bundles on surfaces associated with some pencils ``at infinity''. | |
| dc.description | This is a revised version of a preprint of 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0607677 | |
| dc.identifier | http://arxiv.org/abs/math/0607677 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115147 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C20 | |
| dc.title | Curves having one place at infinity and linear systems on rational surfaces | |
| dc.type | text |