An equidistribution theorem for biraitonal maps of $\mathbb{P}^k$

TL;DR

This paper establishes an equidistribution theorem for positive closed currents under certain birational maps of projective space, expanding understanding of dynamical behavior in complex algebraic geometry.

Contribution

It proves an equidistribution result for positive closed currents for a class of birational maps with specific indeterminacy set conditions.

Findings

Proves equidistribution for a class of birational maps of b2k.

Identifies conditions on indeterminacy sets for equidistribution.

Extends previous results to more general birational maps.

Abstract

We prove an equidistribution theorem of positive closed currents for a certain class of birational maps $f_+:\mathbb{P}^k\to\mathbb{P}^k$ of algebraic degree $d\geq 2$ satisfying $\bigcup_{n\geq 0}f_-^n(I^+)\cap \bigcup_{n\geq 0}f_+^n(I^-)=\emptyset$, where $f_-$ is the inverse of $f_+$ and $I^\pm$ are the sets of indeterminacy for $f_\pm$, respectively.