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On the degree growth of birational mappings in higher dimension

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Abstract

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(x −11 ,..., xd) = (x −11 ,...,x −1 d .We develop a method of regularization and show how it can be used to compute δ for an elementary map.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University Bloomington, 47405, IN

    Eric Bedford

  2. Department of Mathematics, Syracuse University Syracuse, 13244, NY

    Kyounghee Kim

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  1. Eric Bedford
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  2. Kyounghee Kim
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Correspondence to Eric Bedford.

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Communicated by Steven Krantz

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Bedford, E., Kim, K. On the degree growth of birational mappings in higher dimension. J Geom Anal 14, 567–596 (2004). https://doi.org/10.1007/BF02922170

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  • DOI: https://doi.org/10.1007/BF02922170

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