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

Abstract

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.

References in corpus (1)

• Fields of moduli and fields of definition of curves

Cited by in corpus (7)

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• A database of nonhyperelliptic genus 3 curves over Q
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• Distributions of traces of Frobenius for smooth plane curves over finite fields
• Representation of non-special curves of genus 5 as plane sextic curves and its application to finding curves with many rational points
• On the $L$-polynomials of curves over finite fields
• Polarized products of elliptic curves with complex multiplication and field of moduli $\mathbb{Q}$