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Bulletin of the London Mathematical Society 2006 38(6):925-931; doi:10.1112/S0024609306019059
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© Oxford University Press

The Weierstrass Subgroup of a Curve has Maximal Rank

Martine Girard, David R. Kohel and Christophe Ritzenthaler

School of Mathematics and Statistics, The University of Sydney NSW 2006, Australia e-mail: girard{at}maths.usyd.edu.au, e-mail: kohel{at}maths.usyd.edu.au
Institut de Mathématiques de Luminy 163 Avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France e-mail: ritzenth{at}iml.univ-mrs.fr

Received 28 April 2005. Revision received 4 November 2005.

We show that the Weierstrass points of the generic curve of genus g over an algebraically closed field of characteristic 0 generate a group of maximal rank in the Jacobian. 2000 Mathematics Subject Classification 11G30, 14H40, 14H10, 14H55, 14Q05.

The second author thanks the ARC for financial support, and the third author thanks the School of Mathematics and Statistics at the University of Sydney for its warm hospitality.


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