Hyperbolic polarized dynamics, pairs of inverse maps and the Dirichlet property

Jorge Pineiro

Published 2019-09-08Version 1

We explore some intersection properties of divisors associated to polarized dynamical systems on algebraic surfaces. As a consequence, we obtain necessary geometric conditions for the existence of polarizations of hyperbolic type and exhibit compactified divisors associated to automorphisms on K3 surfaces that do not have the Dirichlet property as defined by Moriwaki.