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Journal of the London Mathematical Society 2005 72(3):545-570; doi:10.1112/S0024610705006988
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© The London Mathematical Society

Courbes De Genre 5 Munies D'une Involution Sans Point Fixe

Jean D'almeida, Laurent Gruson and Nicolas Perrin

Université des Sciences et Technologies de Lille AGAT, F-59665 Villeneuve d'Ascq Cedex France
Université de Versailles 45 avenue des États-Unis, F-78035 Versailles France
Institut de Mathématiques de Jussieu 175 rue du Chevaleret, F-75013 Paris France

Received 28 May 2004. Revision received 27 January 2005.

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 P3 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.


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