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Computational aspects of gonal maps and radical parametrization of curves

Abstract : We develop in this article an algorithm that, given a projective curve C, computes a gonal map, that is, a finite morphism from C to P1 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 ≤ 4.
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Joseph Schicho, Frank-Olaf Schreyer, Martin Weimann. Computational aspects of gonal maps and radical parametrization of curves. Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 2013, 24 (5), pp.313-341. ⟨10.1007/s00200-013-0205-0⟩. ⟨hal-02137326⟩

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