Computational aspects of gonal maps and radical parametrization of curves

2013/04/09 by Josef Schicho, Frank–Olaf Schreyer, Frank-Olaf Schreyer +4
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1304.2551

arxiv created 2013/04/09 · openalex publication_date 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

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 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 ≤ 4.

Citations

• green's canonical syzygy conjecture for generic curves of odd genus
• Explicit Solution By Radicals, Gonal Maps and Plane Models of Algebraic Curves of Genus 5 or 6

Related

• Explicit Solution By Radicals, Gonal Maps and Plane Models of Algebraic Curves of Genus 5 or 6
• Syzygies of secant varieties of smooth projective curves and gonality sequences
• Linear syzygies on curves with prescribed gonality
• A note on an effective bound for the gonality conjecture
• The gonality conjecture on syzygies of algebraic curves of large degree