Regular models of hyperelliptic curves

Simone Muselli

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arXiv · 2206.10420

Regular models of hyperelliptic curves

Simone Muselli

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Abstract

Let $K$ be a complete discretely valued field of residue characteristic not $2$ and $O_K$ its ring of integers. We explicitly construct a regular model over $O_K$ with strict normal crossings of any hyperelliptic curve $C/K:y^2=f(x)$. For this purpose, we introduce the new notion of ''MacLane cluster picture'', that aims to be a link between clusters and MacLane valuations.

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Simone Muselli. 2022-06-21. Regular models of hyperelliptic curves. https://arxiv.org/abs/2206.10420

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