Computational aspects of gonal maps and radical parametrization of curves

@article{Schicho2013ComputationalAO,
  title={Computational aspects of gonal maps and radical parametrization of curves},
  author={Josef Schicho and Frank-Olaf Schreyer and M. Weimann},
  journal={Applicable Algebra in Engineering, Communication and Computing},
  year={2013},
  volume={24},
  pages={313-341}
}
We develop in this article an algorithm that, given a projective curve $$C$$ C , computes a gonal map, that is, a finite morphism from $$C$$ C to $$\mathbb P ^1$$ 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… CONTINUE READING