A classification of reduction types of curves

TL;DR

This paper classifies the various reduction types of algebraic curves, detailing their invariants and construction methods for different genera, thus advancing understanding of curve degenerations.

Contribution

It introduces a systematic classification and naming convention for reduction types of algebraic curves of genus greater than one, expanding previous genus-specific results.

Findings

Reduction types form finitely many families for each genus g>1

Construction methods for reduction types are provided

A new naming convention for reduction types is introduced

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.