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arXiv · 2607.07558

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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Edwina Aylward, Lilybelle Cowland Kellock, Vladimir Dokchitser, Elvira Lupoian. 2026-09-15. Reduction Types of Genus 2 Curves. https://arxiv.org/abs/2607.07558

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