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Some remarks on bielliptic and trigonal curves

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arxiv 1512.07963 v1 pith:2CTC2FCY submitted 2015-12-25 math.AG math.CV

Andreas Schweizer This is my paper · ORCID
classification math.AGmath.CV
keywords curvessigmabiellipticfixedgenuspointssomethen
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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 $\sigma$ of prime order $p\geq 5$. If $\sigma$ has no fixed points, then $X$ cannot be trigonal. On the other hand, if $\sigma$ 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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  1. On the Fields of Moduli of Curves of Genus Six

    math.AG 2026-07 conditional novelty 7.0 of 10

    For genus-6 curves, bielliptic curves descend to their field of moduli, and non-descent can only occur for curves on smooth degree-5 del Pezzo surfaces with automorphism group C2 or D10 (with √-1 outside the base fiel...

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