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

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  • Additional Information
    • Publication Date:
      2024
    • Collection:
      ArXiv.org (Cornell University Library)
    • 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. ; Comment: 11 pages
    • Relation:
      http://arxiv.org/abs/2402.00716
    • Online Access:
      http://arxiv.org/abs/2402.00716
    • Accession Number:
      edsbas.E800CF2E