Reduction Types of Genus 2 Curves

Edwina Aylward; Lilybelle Cowland Kellock; Vladimir Dokchitser; Elvira Lupoian

Reduction Types of Genus 2 Curves

Number Theory 2026-07-08 v1 Algebraic Geometry

Authors: Edwina Aylward , Lilybelle Cowland Kellock , Vladimir Dokchitser , Elvira Lupoian

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, N\'eron component group of the Jacobian, conductor exponent, valuation of the discriminant of a minimal Weierstrass model, and cluster pictures.

Keywords

genus 2 curves reduction types Kodaira type Néron component group conductor exponent cluster pictures

Cite

@article{arxiv.2607.07558,
  title  = {Reduction Types of Genus 2 Curves},
  author = {Edwina Aylward and Lilybelle Cowland Kellock and Vladimir Dokchitser and Elvira Lupoian},
  journal= {arXiv preprint arXiv:2607.07558},
  year   = {2026}
}

Comments

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