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arXiv · 2512.09082

A classification of reduction types of curves

Tim Dokchitser
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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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Tim Dokchitser. 2025-12-09. A classification of reduction types of curves. https://arxiv.org/abs/2512.09082

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