Computational aspects of gonal maps and radical parametrization of curves

Joseph Schicho , Frank-Olaf Schreyer , Martin Weimann (1, 2)

1 UNICAEN - Université de Caen Normandie
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Gonal map; canonical curves; scrolls; Betti table; syzygies; special linear series; radical parametrization

Domaines: Mathématiques [math]; Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Joseph Schicho, Frank-Olaf Schreyer, Martin Weimann. Computational aspects of gonal maps and radical parametrization of curves. Applicable Algebra in Engineering, Communication and Computing, 2013, 24 (5), pp.313-341. ⟨10.1007/s00200-013-0205-0⟩. ⟨hal-02137326⟩