The birational invariants of Lins Neto’s foliations

Abstract

Lins Neto [Ann. Sci. École Norm. Sup. (4) 35 (2002), pp. 231–266] constructed families of foliations which are counterexamples to Poincaré’s Problem and Painlevé’s Problem. We will determine the minimal models of these families of foliations, calculate their Chern numbers, Kodaira dimension, and numerical Kodaira dimension. We prove that the slopes of Lins Neto’s foliations are at least 6, and their limits are bigger than 7 7 .