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Effective radical parametrization of trigonal curves

By Josef Schicho and David Sevilla


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.Comment: 11 pages, a previous extended abstract is arXiv:1103.468

Topics: Mathematics - Algebraic Geometry, Computer Science - Symbolic Computation, 14H51, 68W30 (Primary) 17B45 (Secondary)
Year: 2011
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