Effective radical parametrization of trigonal curves

Details Effective radical parametrization of trigonal curves Effective radical parametrization of trigonal curves

2011-04-13

arxiv.org/abs/1104.2470v1

Mathematics

Algebraic Geometry

11 pages, a previous extended abstract is arXiv:1103.4689

Scientific paper

Let $C$ be a non-hyperelliptic algebraic curve. It is known that its canonical image is the intersection of the quadrics that contain it, except when $C$ is trigonal (that is, it has a linear system of degree 3 and dimension 1) or isomorphic to a plane quintic (genus 6). In this context, we present a method to decide whether a given algebraic curve is trigonal, and in the affirmative case to compute a map from $C$ to the projective line whose fibers cut out the linear system.

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