Regular models of hyperelliptic curves

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 $C/K:y^2=f\left(x\right)$. For this purpose, we introduce the new notion of MacLane cluster picture, that aims to be a link between clusters and MacLane valuations.