Normal generation of line bundles on multiple coverings

Details Normal generation of line bundles on multiple coverings Normal generation of line bundles on multiple coverings

2008-09-13

arxiv.org/abs/0809.2312v1

Mathematics

Algebraic Geometry

17 pages, 6 figures

Scientific paper

Any line bundle $\cl $ on a smooth curve $C$ of genus $g$ with $\deg \cl \ge 2g+1$ is normally generated, i.e., $\varphi_\cl (C)\subseteq \mathbb P H^0 (C,\cl)$ is projectively normal. However, it has known that more various line bundles of degree $d$ failing to be normally generated appear on multiple coverings of genus $g$ as $d$ becomes smaller than $2g+1$. Thus, investigating the normal generation of line bundles on multiple coverings can be an effective approach to the normal generation. In this paper, we obtain conditions for line bundles on multiple coverings being normally generated or not, respectively.

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