Comparison of dynamical degrees for semi-conjugate meromorphic maps

Abstract

Let $f\colon X\rightarrow X$ be a dominant meromorphic map on a projective manifold $X$ which preserves a meromorphic fibration $\pi\colon X\rightarrow Y$ of $X$ over a projective manifold $Y$. We establish formulas relating the dynamical degrees of $f$, the dynamical degrees of $f$ relative to the fibration and the dynamical degrees of the map $g\colon Y\rightarrow Y$ induced by $f$. Applications are given.