An example of a topologically non-rigid foliation of the complex projective plane

TL;DR

This paper presents an explicit algebraic family of foliations on the complex projective plane that are topologically trivial but not analytically trivial, highlighting the importance of certain assumptions in a rigidity theorem.

Contribution

It provides a concrete example demonstrating the distinction between topological and analytical triviality in foliations, challenging existing assumptions in rigidity results.

Findings

Explicit example of a topologically trivial but analytically non-trivial foliation

Highlights the necessity of assumptions in Y. Ilyashenko's rigidity theorem

Shows the difference between topological and analytical triviality in complex foliations

Abstract

We give here an explicit example of an algebraic family of foliations of CP^{2} which is topologically trivial but not analytically trivial. This example underlines the necessity of some assumptions in Y. Ilyashenko's rigidity theorem.