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

초록

It is known that for a holomorphic endomorphism of ${\mathbb{P}}^k$ or a regular polynomial automorphism of ${\mathbb{C}}^k$, under certain conditions given in terms of the mapping, the normalized pull-backs of a given positive closed current $(p,p)$ of unit mass converges to the Green $(p,p)$-current associated with the given map where $1\le p\le k$. In this talk, we study the inverse images of positive closed currents of bidegree $(p,p)$ under regular birational maps. More precisely, we discuss a sufficient condition that a sequence of normalized pull-backs of a given current converges to the Green $(p,p)$-current.