Regular models of superelliptic curves via Mac Lane valuations

Let X  P^1 be a Z/n-branched cover over a complete discretely valued field K, where n does not divide the residue characteristic of K.  We explicitly construct the minimal regular normal crossings model of X over the valuation ring of K.  By “explicitly”, we mean that we construct a normal model of P^1 whose normalization in K(X) is the desired regular model.  The normal model of P^1 is fully encoded as a basket of finitely many discrete valuations on the rational function field K(P^1), each of which is given using Mac Lane’s 1936 notation involving finitely many polynomials and rational numbers (no familiarity with Mac Lane’s notation will be assumed)!.  This is joint work with Padmavathi Srinivasan.