Mathematical Research Letters

Volume 27 (2020)

Number 2

On degrees of birational mappings

Pages: 319 – 337

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n2.a1

Authors

Serge Cantat (CNRS, IRMAR, UMR 6625, Université de Rennes, France)

Junyi Xie (CNRS, IRMAR, UMR 6625, Université de Rennes, France)

Abstract

We prove that the degrees of the iterates $\deg (f^n)$ of a birational map satisfy $\liminf(\deg (f^n)) \lt + \infty$ if and only if the sequence $\deg (f^n)$ is bounded, and that the growth of $\deg (f^n)$ cannot be arbitrarily slow, unless $\deg (f^n)$ is bounded.

Accepted 6 January 2019

Published 8 June 2020