Models of hyperelliptic curves with tame potentially semistable reduction

Abstract

Let C be a hyperelliptic curve y2=f(x) over a discretely valued field K . The p ‐adic distances between the roots of f(x) can be described by a completely combinatorial object known as the cluster picture. We show that the cluster picture of C , along with the leading coefficient of f and the action of Gal(K¯/K) on the roots of f , completely determines the combinatorics of the special fibre of the minimal strict normal crossings model of C . In particular, we give an explicit description of the special fibre in terms of this data.