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arXiv · 2402.00716

A census of genus 6 curves over $\mathbb{F}_2$

Yongyuan Huang·Kiran S. Kedlaya·Jun Bo Lau
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Abstract

We compile a complete list of isomorphism class representatives of curves of genus 6 over $\mathbb{F}_2$. We use explicit descriptions of canonical curves in each stratum of the Brill--Noether stratification of the moduli space $\mathcal{M}_6$, due to Mukai in the generic case. Our computed value of $\#\mathcal{M}_6(\mathbb{F}_2)$ agrees with the Lefschetz trace formula as recently computed by Bergstrom--Canning--Petersen--Schmitt.

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Yongyuan Huang, Kiran S. Kedlaya, Jun Bo Lau. 2024-02-01. A census of genus 6 curves over $\mathbb{F}_2$. https://arxiv.org/abs/2402.00716

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