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 |