A classification of reduction types of curves

2025/12/09 by Tim Dokchitser, Dokchitser, Tim
Mathematics · #14H10 #14H20 #14H25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #Primary 11G20 #Secondary 11G30

paper · pdf · doi:10.48550/arxiv.2512.09082

openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus g>1, they form finitely many families, and we explain how to construct them, and introduce a naming convention.

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