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Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields

Part of: General commutative ring theory Computational aspects in algebraic geometry Curves

Published online by Cambridge University Press:  01 August 2014

Reynald Lercier ,
Christophe Ritzenthaler ,
Florent Rovetta  and
Jeroen Sijsling
Reynald Lercier
Affiliation:
DGA MI, La Roche Marguerite, 35174 Bruz , France Institut de recherche mathématique, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France email reynald.lercier@m4x.org
Christophe Ritzenthaler
Affiliation:
Institut de recherche mathématique, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France email christophe.ritzenthaler@univ-rennes1.fr
Florent Rovetta
Affiliation:
Institut de Mathématiques de Luminy, UMR 6206 du CNRS, Luminy, Case 907, 13288 Marseille, France email florent.rovetta@univ-amu.fr
Jeroen Sijsling
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, United Kingdom email sijsling@gmail.com

Abstract

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We study new families of curves that are suitable for efficiently parametrizing their moduli spaces. We explicitly construct such families for smooth plane quartics in order to determine unique representatives for the isomorphism classes of smooth plane quartics over finite fields. In this way, we can visualize the distributions of their traces of Frobenius. This leads to new observations on fluctuations with respect to the limiting symmetry imposed by the theory of Katz and Sarnak.

MSC classification

Secondary: 14Q05: Curves 13A50: Actions of groups on commutative rings; invariant theory 14H10: Families, moduli (algebraic) 14H37: Automorphisms
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 128 - 147
Copyright
© The Author(s) 2014 

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