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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
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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

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