Reduction of Hyperelliptic Curves in Residue Characteristic 2

Fuente: arXiv
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Main Authors: Gehrunger, Tim, Pink, Richard
Format: Preprint
Published: 2024
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author Gehrunger, Tim
Pink, Richard
author_facet Gehrunger, Tim
Pink, Richard
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_14214
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Reduction of Hyperelliptic Curves in Residue Characteristic 2
Gehrunger, Tim
Pink, Richard
Algebraic Geometry
Number Theory
14H30 (Primary) 14H10, 11G20 (Secondary)
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.
title Reduction of Hyperelliptic Curves in Residue Characteristic 2
topic Algebraic Geometry
Number Theory
14H30 (Primary) 14H10, 11G20 (Secondary)
url https://arxiv.org/abs/2404.14214