Title: Conductors and minimal discriminants of hyperelliptic curves: a comparison in the tame case
Abstract: Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In genus one, the Ogg–Saito formula shows that these two invariants are equal, and in genus two, Qing Liu showed that they are related by an inequality. We extend Liu’s inequality to hyperelliptic curves of arbitrary genus assuming that the residue characteristic is large compared to the genus. The key ingredients in this proof are an explicit analysis of regular models arising from Jung’s method of resolving surface singularities, and an understanding of the behaviour of associated metric trees under a natural inductive process.