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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Group generated by the Weierstrass points of a plane quartic


Authors: Martine Girard and Pavlos Tzermias
Journal: Proc. Amer. Math. Soc. 130 (2002), 667-672
MSC (1991): Primary 11G30, 14H25; Secondary 14H45
Published electronically: August 29, 2001
MathSciNet review: 1866017
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Abstract: We describe the group generated by the Weierstrass points in the Jacobian of the curve $X^4+Y^4+Z^4+3 \,(X^2 Y^2+X^2 Z^2+Y^2 Z^2) =0.$ This curve is the only curve of genus 3, apart from the fourth Fermat curve, possessing exactly twelve Weierstrass points.


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Additional Information

Martine Girard
Affiliation: Théorie des Nombres, Institut de Mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
Email: girard@math.jussieu.fr

Pavlos Tzermias
Affiliation: Department of Mathematics, The University of Arizona, P.O. Box 210089, 617 N. Santa Rita, Tucson, Arizona 85721-0089
Address at time of publication: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
Email: tzermias@math.arizona.edu, tzermias@math.utk.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06193-7
PII: S 0002-9939(01)06193-7
Keywords: Algebraic curves, Jacobians, Weierstrass points
Received by editor(s): September 18, 2000
Published electronically: August 29, 2001
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society