Periodic points for meromorphic self-maps of Fujiki varieties

Abstract

Let $f\colon X\to X$ be a dominant meromorphic self-map of a compact complex variety $X$ in the Fujiki class $\mathcal{C}$. If the topological degree of $f$ is strictly larger than the other dynamical degrees of $f$, we show that the number of isolated $f$-periodic points grows exponentially fast similarly to the topological degrees of the iterates of $f$; in particular, we give a positive answer to a conjecture of Shou-Wu Zhang. In the general case, we show that the exponential growth of the number of isolated $f$-periodic points is at most the algebraic entropy of $f$.