Computational aspects of gonal maps and radical parametrization of curves
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 \(\mathbb P ^1\) 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 \(\le 4\).
gonal map radical parametrization syzygies canonical curves scrolls betti table special linear series