Webs invariant by rational maps on surfaces

TL;DR

This paper proves that rational maps on surfaces that preserve webs are of Lattès type under mild conditions and classifies web-preserving endomorphisms of the projective plane, extending previous classifications.

Contribution

It establishes that web-preserving rational maps are of Lattès type and extends classification results for endomorphisms of P^2.

Findings

Web-preserving rational maps are of Lattès type.

Classification of web-preserving endomorphisms of P^2 extended.

Provides conditions under which rational maps preserve webs.

Abstract

We prove that under mild hypothesis rational maps on a surface preserving webs are of Latt\`es type. We classify endomorphisms of P^2 preserving webs, extending former results of Dabija-Jonsson.