The Journal of Geometric Analysis

, Volume 14, Issue 4, pp 567–596

On the degree growth of birational mappings in higher dimension


DOI: 10.1007/BF02922170

Cite this article as:
Bedford, E. & Kim, K. J Geom Anal (2004) 14: 567. doi:10.1007/BF02922170


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.

Math Subject Classifications


Key Words and Phrases

Birational mapdegree complexity

Copyright information

© Mathematica Josephina, Inc. 2004

Authors and Affiliations

  1. 1.Department of MathematicsIndiana University Bloomington
  2. 2.Department of MathematicsSyracuse University Syracuse