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TitleExplicit solution by radicals, gonal maps and plane models of algebraic curves of genus 5 or 6
Author(s) Michael Harrison
TypeArticle in Journal
AbstractWe 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.
KeywordsAlgebraic curves, Radical parametrisation, Gonality, Plane models
URL http://www.sciencedirect.com/science/article/pii/S0747717112001125
JournalJournal of Symbolic Computation
Pages3 - 21
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No