Semi-continuity of dynamical degrees

To any birational automorphism we can associate its dynamical degree. This is a number characterising the growth of any ample class under iteration of the automorphism. If the automorphism is regular, then its dynamical degree equals the absolute value of the greatest eigenvalue of the action of the inverse image on the Neron-Severi group of the variety.
If we fix a family of birational automorphisms, then the dynamical degree defines a function on the base of the family. I am going to tell the proof of Xie Junyi's theorem that in the case of a family of surface birational automorphisms this function is lower semi-continuous.