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PreprintCC BY 4.0arXiv

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

  • Samuel Grushevsky
  • Christophe Ritzenthaler
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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.

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Cite

BibTeXRIS
BibTeX
@misc{grushevsky2026complete,
  title = {{A complete curve of genus 5 in the moduli space of curves of genus 3 and related questions}},
  author = {Samuel Grushevsky and Christophe Ritzenthaler},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.13486},
  eprint = {2607.13486},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.13486},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A complete curve of genus 5 in the moduli space of curves of genus 3 and related questions
AU  - Samuel Grushevsky
AU  - Christophe Ritzenthaler
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2607.13486
UR  - https://arxiv.org/abs/2607.13486
AB  - 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.
ER  -