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

@inproceedings{Lercier2014ParametrizingTM, title={Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields}, author={Reynald Lercier and Christophe Ritzenthaler and Florent Ulpat Rovetta and Jeroen Sijsling}, year={2014} }

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.

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## Plane quartics over Q with complex multiplication

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## On twists of smooth plane curves

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## Reduction type of genus-3 curves in a special stratum of their moduli space

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## Bielliptic smooth plane curves and quadratic points

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