These are expanded lecture notes for the summer school on Berkovich spaces that took
place at the Institut de Mathématiques de Jussieu, Paris, during June 28–July 9, 2010. They …

We study the dynamics in C2 of superattracting fixed point germs and of polynomial maps
near infinity. In both cases we show that the asymptotic attraction rate is a quadratic integer …

We find good dynamical compactifications for arbitrary polynomial map**s of C² and use
them to show that the degree growth sequence satisfies a linear integral recursion formula …

Given an integral domain A, a monic polynomial P of degree n with coe cients in A and a
divisor d of n, invertible in A, there is a unique monic polynomial Q such that the degree of …

The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized
by non-negative rational numbers. As the rational number increases the corresponding …

In the last decades, cones associated to varieties have been a basic tool to approach the
theory of minimal models. Although this theory works in the case of smooth surfaces by …

We consider pencils at infinity V=〈 F, Zd〉 in the projective plane P2. There exists a minimal
composition of point blowing ups XV→ P2 eliminating the indeterminacies of the rational …

This paper is devoted to determine the geometry of a class of smooth projective rational
surfaces whose minimal models are the Hirzebruch ones; concretely, they are obtained as …

Let Z be a smooth projective rational surface. A condition that implies the polyhedrality of the
cone of curves of Z is given. This one depends only on the configuration of infinitely near …

We study the class of planar polynomial vector fields admitting Darboux first integrals of the
type∏ i= 1 rfi α i, where the α i's are positive real numbers and the fi's are polynomials …