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October 2, 20250 citationsOpen Access

Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2

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TGTim Gehrunger

Key Points

  • The study demonstrates general properties of stable reduction for hyperelliptic curves of genus g.
  • Researchers worked through explicit examples for hyperelliptic curves up to genus 30, enhancing understanding.
  • Algorithm refinements improve the computation of stable reductions in residue characteristic 2.
  • Valuation techniques are utilized to analyze marked curves with their Weierstrass points across varying genus levels.

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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Cite This Study

Tim Gehrunger (2025) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bf48https://doi.org/10.48550/arxiv.2506.19663
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