Canonical heights for plane polynomial maps of small topological degree

Abstract

We study canonical heights for plane polynomial mappings of small topological degree. In particular, we prove that for points of canonical height zero, the arithmetic degree is bounded by the topological degree and hence strictly smaller than the first dynamical degree. The proof uses the existence, proved by Favre and the first author, of certain compactifications of the plane adapted to the dynamics.

arXiv commentModified title and some references in response to the new version of the paper by Silverman. 10 pages. To appear in Math. Res. Lett