Strict germs on normal surface singularities

Abstract

We show that any holomorphic germ $f:(X,x_0)\to (Y,y_0)$ of topological degree $1$ between normal surface singularities can be written as $f=\ddot{I}€\circ \ddot{I}ƒ$, where $\ddot{I}€:Y^{\prime }\to (Y,y_0)$ is a modification and $\ddot{I}ƒ:(X,x_0)\to (Y^{\prime },y_1)$ is a local isomorphism sending $x_0$ to a point $y_1\in \ddot{I}{€}^{-1}(y_0)$. A result by Fantini, Favre and myself guarantees that when $f$ is a selfmap, then $(X,x_0)$ is a sandwiched singularity. We give here an alternative proof based on the construction of the associated Kato surfaces, and valuative dynamics.

22 pages, 2 figures