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A complete curve of genus 5 in the moduli space of curves of genus 3 and related questions

Year: 2026

Type: preprint

Abstract: Let M_3 be the coarse moduli space of smooth complex projective curves of genus 3. Through a general point of M_3, we construct a smooth complete curve of genus 21 and gonality 7, and a singular complete curve whose normalization has genus 19 and gonality 6. We also construct a Hodge-generic complete trigonal curve of geometric genus 5 in M_3.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.13486

Authors: Grushevsky, Samuel, Ritzenthaler, Christophe

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7169098403

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