A complete curve of genus 10 in the moduli space of curves of genus 3 and related questions

Samuel Grushevsky; Christophe Ritzenthaler

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arXiv · 2607.13486

A complete curve of genus 10 in the moduli space of curves of genus 3 and related questions

Samuel Grushevsky·Christophe Ritzenthaler

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Abstract

We show the existence of a complete trigonal curve of geometric genus 10 in the moduli space $\mathcal{M}_3$ of smooth complex projective curves of genus $3$, and of a complete curve of geometric genus 102 through a general point of $\mathcal{M}_3$. We also show that the moduli space $\mathcal{A}_3$ of principally polarized complex abelian threefolds contains a complete curve whose normalization is a hyperelliptic curve of genus 4.

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Samuel Grushevsky, Christophe Ritzenthaler. 2026-07-15. A complete curve of genus 10 in the moduli space of curves of genus 3 and related questions. https://arxiv.org/abs/2607.13486

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