Foliations invariant by rational maps

TL;DR

This paper classifies pairs of holomorphic foliations and rational maps on projective surfaces, showing that both are integrable when the map preserves the foliation, advancing understanding of their structure and invariance properties.

Contribution

It provides a classification of foliations invariant under rational maps on projective surfaces, demonstrating their integrability and revealing new structural insights.

Findings

Both the rational map and foliation are integrable when the map preserves the foliation.

The classification characterizes pairs (F, f) with invariant foliations under rational maps.

The results deepen understanding of the interplay between foliations and rational maps on surfaces.

Abstract

We give a classification of pairs (F, f) where F is a holomorphic foliation on a projective surface and f is a non-invertible dominant rational map preserving F. We prove that both the map and the foliation are integrable in a suitable sense.