An asymptotic existence theorem for plane curves with prescribed singularities
| dc.creator | Mignon, Thierry | |
| dc.date | 1999-04-19 | |
| dc.date | 2000-02-05 | |
| dc.date.accessioned | 2026-07-07T05:28:45Z | |
| dc.date.available | 2026-07-07T05:28:45Z | |
| dc.description | Let $d,m_1,...,m_r$ be ($r+1$) positive integers, and $P_1,...,P_r$ be $r$ general points in the projective plane ; let $m$ be a positive integer. We prove that there exists a bound $d_0(m)$ such that : If $m_i < m$ ($0<i<r+1$), and $d > d_0(m)$ then the linear system $L$ of plane curves of degree $d$ having a multiplicity at least $m_i$ at each point $P_i$ has the expected dimension ; moreover, if $L$ is not empty, there exists an irreducible plane curve of degree $d$, smooth away from the $r$ points $P_i$, and having an ordinary singularity of the prescribed multiplicity $m_i$ at each point $P_i$. This curve may be isolated in $L$. | |
| dc.description | 16 pages, Latex; corrections in sections 3 and 5, misprints removed | |
| dc.identifier | https://arxiv.org/abs/math/9904097 | |
| dc.identifier | http://arxiv.org/abs/math/9904097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78376 | |
| dc.subject | Algebraic Geometry | |
| dc.title | An asymptotic existence theorem for plane curves with prescribed singularities | |
| dc.type | text |