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arXiv · 1512.07963

Some remarks on bielliptic and trigonal curves

Andreas Schweizer
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Abstract

We prove some results on algebraic curves $X$ of genus $g\geq 2$ in characteristic $0$. For example: Assume that $X$ has an automorphism $σ$ of prime order $p\geq 5$. If $σ$ has no fixed points, then $X$ cannot be trigonal. On the other hand, if $σ$ has fixed points, then $X$ is bielliptic only if it belongs to one of three extremal types of curves of small genus.

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Andreas Schweizer. 2015-12-25. Some remarks on bielliptic and trigonal curves. https://arxiv.org/abs/1512.07963

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