A classification of reduction types of curves
Algebraic Geometry
2025-12-11 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.2512.09082,
title = {A classification of reduction types of curves},
author = {Tim Dokchitser},
journal= {arXiv preprint arXiv:2512.09082},
year = {2025}
}
Comments
1st version; 58 pages; Comments and suggestions very welcome!