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Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2

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arxiv 2506.19663 v1 pith:KXPV5HPJ submitted 2025-06-24 math.AG math.NT

Tim Gehrunger This is my paper · ORCID
classification math.AGmath.NT
keywords characteristiccurvegenushyperellipticmarkedreductionresiduestable
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abstract

Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We prove some general properties of the stable reduction of this marked curve for a valuation of residue characteristic $2$ and refine an existing algorithm for its computation. We work out explicit examples up to genus $g=30$.

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  1. Semistable reduction of smooth quartics

    math.AG 2026-06 conditional novelty 4.0 of 10

    For smooth plane quartics, non-hyperelliptic stable reduction is equivalent to the existence of a unique GIT-stable plane model, and the stable model is obtained by cusp resolution.

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