On the Degree Growth of Birational Mappings in Higher Dimension

Eric Bedford, Kyounghee Kim

Let $f$ be a birational map of ${\mathbf{C}}^d$, and consider the degree complexity, or asymptotic degree growth rate $\delta (f)={\lim }_{n\to \infty }(\mathrm{deg}(f^n){)}^{1/n}$. We introduce a fami…