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Non-trivial Linear Systems on Smooth Plane Curves
- Publication Year :
- 1993
- Publisher :
- arXiv, 1993.
-
Abstract
- 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.<br />Comment: 15 pages, LaTeX 2.09
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....091c1fe9b9c2783cf1372326efd62019
- Full Text :
- https://doi.org/10.48550/arxiv.alg-geom/9301003