| Title | Explicit solution by radicals, gonal maps and plane models of algebraic curves of genus 5 or 6 |
| Author(s) | Michael Harrison |
| Type | Article in Journal |
| Abstract | We give explicit computational algorithms to construct minimal degree (always ⩽4) ramified covers of P 1 for algebraic curves of genus 5 and 6. This completes the work of Schicho and Sevilla (who dealt with the g ⩽ 4 case) on constructing radical parametrisations of arbitrary genus g curves. Zariski showed that this is impossible for the general curve of genus ⩾7. We also construct minimal degree birational plane models and show how the existence of degree 6 plane models for genus 6 curves is related to the gonality and geometric type of a certain auxiliary surface. |
| Keywords | Algebraic curves, Radical parametrisation, Gonality, Plane models |
| ISSN | 0747-7171 |
| URL |
http://www.sciencedirect.com/science/article/pii/S0747717112001125 |
| Language | English |
| Journal | Journal of Symbolic Computation |
| Volume | 51 |
| Number | 0 |
| Pages | 3 - 21 |
| Year | 2013 |
| Note | Effective Methods in Algebraic Geometry |
| Edition | 0 |
| Translation |
No |
| Refereed |
No |
