arXiv subjects

Florent Rovetta

Publications and source records attributed to Florent Rovetta.

2 recordsLinked to original sources

arXiv2019

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

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.

math.AG↗

arXiv2015

Distributions of traces of Frobenius for smooth plane curves over finite fields

In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus $3$ curves over small finite fields. In the present one, we give a heuristic explanation of these data, by extrapolating from results on the distribution of traces of Frobenius for plane curves whose degree is small with respect to the cardinality of their finite base field. In particular, our methods shed some new light on the asymmetry of the distribution around its mean value, which is related to the Serre obstruction.

math.AG↗