We study properties of the space of irreducible germs of plane curves (branches), seen as an ultrametric space. We provide various geometrical methods to measure the distance between two branches and to compare distances ...

This is an extended abstract with some of the results that will appear in the forthcoming paper [1] in which we characterize when a given complete ideal in a two-dimensional local ring with a rational singularity can be ...

We prove that the genus g, the relative irregularity q_f and the Clifford index c_f of a non-isotrivial fibration f satisfy the inequality q_f=g-c_f. This gives in particular a proof of Xiao’s conjecture for fibrations ...