On the Degree Growth of Birational Mappings in Higher Dimension

Details On the Degree Growth of Birational Mappings in Higher Dimension On the Degree Growth of Birational Mappings in Higher Dimension

2004-06-30

arxiv.org/abs/math/0406621v2

Mathematics

Dynamical Systems

Scientific paper

Let $f$ be a birational map of ${\bf C}^d$, and consider the degree complexity, or asymptotic degree growth rate $\delta(f)=\lim_{n\to\infty}({\rm deg}(f^n))^{1/n}$. We introduce a family of elementary maps, which have the form $f=L\circ J$, where $L$ is (invertible) linear, and $J(x_1,...,x_d)=(x_1^{-1},...,x_d^{-1})$. We develop a method of regularization and show how it can be used to compute $\delta$ for an elementary map.

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