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arXiv · 1304.2551

Computational aspects of gonal maps and radical parametrization of curves

Josef Schicho·Frank-Olaf Schreyer·Martin Weimann
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Abstract

We develop in this article an algorithm that, given a projective curve $C$, computes a \textit{gonal map}, that is, a finite morphism from $C$ to the projective line of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality $\le 4$.

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Josef Schicho, Frank-Olaf Schreyer, Martin Weimann. 2013-04-09. Computational aspects of gonal maps and radical parametrization of curves. https://arxiv.org/abs/1304.2551

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