%0 Journal Article %T Lins Neto's examples of foliations and the Mori cone of blow-ups of $P^2$ %A Francisco Monserrat %J Mathematics %D 2009 %I arXiv %R 10.1112/blms/bdq111 %X We use a family of algebraic foliations given by A. Lins Neto to provide new evidences to a conjecture, related to the Harbourne-Hirschowitz's one and implying the Nagata's conjecture, which concerns the structure of the Mori cone of blow-ups of $\mathbb{P}^2$ at very general points. %U http://arxiv.org/abs/0901.1565v2