Non-trivial Linear Systems on Smooth Plane Curves
| dc.creator | Coppens, Marc | |
| dc.creator | Kato, Takao | |
| dc.date | 1993-01-06 | |
| dc.date.accessioned | 2026-07-07T09:05:47Z | |
| dc.date.available | 2026-07-07T09:05:47Z | |
| dc.description | Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically closed field $k$. A base point free complete very special linear system $g^r_n$ on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor $E$ on $C$ of degree $md-n$ such that $g^r_n=|mg^2_d-E|$ and $r=(m^2+3m)/2-(md-n)$. In this paper, we prove the following: Theorem Let $g^r_n$ be a base point free very special non-trivial complete linear system on $C$. Write $r=(x+1)(x+2)/2-b$ with $x, b$ integers satisfying $x\ge 1, 0\le b \le x$. Then $n\ge n(r):=(d-3)(x+3)-b$. Moreover, this inequality is best possible. | |
| dc.description | 15 pages, LaTeX 2.09 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9301003 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9301003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149793 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Non-trivial Linear Systems on Smooth Plane Curves | |
| dc.type | text |