Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T02:46:37.223Z Has data issue: false hasContentIssue false
  • English
  • Français

COURBES DE GENRE 5 MUNIES D'UNE INVOLUTION SANS POINT FIXE

Published online by Cambridge University Press:  08 December 2005

JEAN D'ALMEIDA ,
LAURENT GRUSON  and
NICOLAS PERRIN
JEAN D'ALMEIDA
Affiliation:
Université des Sciences et Technologies de Lille, AGAT, F-59665 Villeneuve d'Ascq Cedex France
LAURENT GRUSON
Affiliation:
Université de Versailles, 45 avenue des États-Unis, F-78035 Versailles France
NICOLAS PERRIN
Affiliation:
Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, F-75013 Paris France
Get access

Abstract

We study genus 5 curves C with a fixed point free involution. We give a geometrical (embedded) characterisation of these curves among all genus 5 curves: the points of the Prym variety associated to the involution give embeddings of the curve C in ${{\mathbb P}}_3$ so that C has infinitely many quadrisecant lines. Conversely, any genus 5 curve having such an embedding is endowed with a fixed point free involution and the embedding is given by a point of the Prym variety.

Keywords

14H4014H45
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 545 - 570
Copyright
The London Mathematical Society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)