Equidistribution of positive closed currents for certain birational maps of P^k

초록

In this talk, we will consider birational maps f^+: P^k -> P^k with a certain splitting conditions in terms of indeterminacy sets for f^+-. For more information about this class, we refer the reader to [3]. This class of birational maps can be considered as a natural generalization of birational maps induced from a regular polynomial automorphism of C^k. We will discuss a generalization of an equidistribution theorem for regular polynomial automorphisms of C^k to birational maps of this class. More precisely, we will find a sufficient condition of a positive closed (p, p)-current S of unit mass on P^k in terms of the set of indeterminacy of f^- so that the sequence of properly normalized pull-backs d^{?pn}(f^n)^?S of S converges to the Green (p, p)-current.