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Mathematics of Computation

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The group of Weierstrass points of a plane quartic with at least eight hyperflexes

Author: Martine Girard
Journal: Math. Comp. 75 (2006), 1561-1583
MSC (2000): Primary 11G30, 14H55, 14Q05; Secondary 14H40
Published electronically: May 1, 2006
MathSciNet review: 2219046
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Abstract: The group generated by the Weierstrass points of a smooth curve in its Jacobian is an intrinsic invariant of the curve. We determine this group for all smooth quartics with eight hyperflexes or more. Since Weierstrass points are closely related to moduli spaces of curves, as an application, we get bounds on both the rank and the torsion part of this group for a generic quartic having a fixed number of hyperflexes in the moduli space $ \mathcal{M}_{3}$ of curves of genus 3.

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Additional Information

Martine Girard
Affiliation: Universiteit Leiden, Mathematisch Instituut, 2300 R. A. Leiden, The Netherlands
Address at time of publication: School of Mathematics and Statistics, The University of Sydney, New South Wales, NSW 2006, Australia

Keywords: Algebraic curves, Jacobian, Weierstrass points, quartics, elliptic curves.
Received by editor(s): March 6, 2003
Received by editor(s) in revised form: April 1, 2005
Published electronically: May 1, 2006
Additional Notes: This research was carried out while the author was a postdoctoral fellow at Leiden University within the European Research Training Network Galois Theory and Explicit Methods in Arithmetic.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.