Submission date: 2 January 2018

Abstract:

In this article we use techniques developed by Hrushovski-Loeser to study certain metric properties of the Berkovich analytification of a finite morphism of smooth connected projective curves. In recent work, M. Temkin proved a radiality statement for the topological ramification locus associated to such finite morphisms. We generalize this result in two directions. We prove a radiality statement for a more general class of sets which we call definable sets. In another direction, we show that the result of Temkin can be obtained in families.

Mathematics Subject Classification: 14G22, 14T05, 03C98

Keywords and phrases:

Full text arXiv 1801.00550: pdf, ps.