Reynald Lercier

R. Lercier, C. Ritzenthaler, F. Rovetta, and J. Sijsling. 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 Mathematical Society. To appear.

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.

[ bib | preprint | publication ] Back