On the degree growth of birational mappings in higher dimension
- Cite this article as:
- Bedford, E. & Kim, K. J Geom Anal (2004) 14: 567. doi:10.1007/BF02922170
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Let ƒ be a birational map of Cd,and consider the degree complexity or asymptotic degree growth rate δ(ƒ) = limn → ∞ (deg(ƒn))1/n.We introduce a family of elementary maps, which have the form ƒ = L o J, where L is (invertible) linear, and J(x1−1,..., xd) = (x1−1,...,xd−1.We develop a method of regularization and show how it can be used to compute δ for an elementary map.