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PreprintCC BY 4.0arXiv

Reduction Types of Genus 2 Curves

  • Edwina Aylward
  • Lilybelle Cowland Kellock
  • Vladimir Dokchitser
  • Elvira Lupoian
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Abstract

Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tables for curves of genus 2. The invariants addressed include: reduction type of the minimal regular model, reduction type of the minimal regular model with normal crossings, Néron component group of the Jacobian, conductor exponent, valuation of the discriminant of a minimal Weierstrass model, and cluster pictures.

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Cite

BibTeXRIS
BibTeX
@misc{aylward2026reduction,
  title = {{Reduction Types of Genus 2 Curves}},
  author = {Edwina Aylward and Lilybelle Cowland Kellock and Vladimir Dokchitser and Elvira Lupoian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.07558},
  eprint = {2607.07558},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.07558},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Reduction Types of Genus 2 Curves
AU  - Edwina Aylward
AU  - Lilybelle Cowland Kellock
AU  - Vladimir Dokchitser
AU  - Elvira Lupoian
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2607.07558
UR  - https://arxiv.org/abs/2607.07558
AB  - Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tables for curves of genus 2. The invariants addressed include: reduction type of the minimal regular model, reduction type of the minimal regular model with normal crossings, Néron component group of the Jacobian, conductor exponent, valuation of the discriminant of a minimal Weierstrass model, and cluster pictures.
ER  -