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Reduction of Hyperelliptic Curves in Residue Characteristic 2

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arxiv 2404.14214 v2 pith:R6HIPYRP submitted 2024-04-22 math.AG math.NT

Tim Gehrunger , Richard Pink This is my paper · ORCID
classification math.AGmath.NT
keywords characteristiccurvereductionhyperellipticmarkedresiduealgorithmcases
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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 present an explicit algorithm to compute the stable reduction of this marked curve for a valuation of residue characteristic $2$ over a finite extension of $K$. In the cases $g\le2$ we work out relatively simple conditions for the structure of this reduction.

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  1. Invariants recovering the reduction type of a hyperelliptic curve

    math.NT 2025-02 accept novelty 7.0 of 10

    Valuations of a finite, genus-dependent list of explicitly defined absolute invariants determine the stable model tree and therefore the dual graph of the special fibre of a semistable hyperelliptic curve over a local...

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