Parametrizing the moduli space of curves and
applications to smooth plane quartics over finite fields.
In Jung Hee Cheon and Hyang-Sook Lee, editors,
Proceedings of the Algorithmic Number Theory Symposium ANTS-XI, LMS Journal
of Computation and Mathematics, GyeongJu, South Korea, August 2014. London
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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