Work

Reduction Types of Genus 2 Curves

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.07558

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

Institutions: University College London, University of Manchester

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface: London School of Geometry and Number Theory, DTP 2224 University College London, DTP 2224 University of Manchester

OpenAlex ID: W7167820319

Cites: 1

Cited by: 1

Related to: 10