Convex foliations of degree 4 on the complex projective plane

Abstract

We show that up to automorphism of $${\mathbb {P}}^{2}_{{\mathbb {C}}}$$ there are 5 homogeneous convex foliations of degree four on $${\mathbb {P}}^{2}_{{\mathbb {C}}}.$$ Using this result, we give a partial answer to a question posed in 2013 by Marin and Pereira about the classification of reduced convex foliations on $${\mathbb {P}}^{2}_{{\mathbb {C}}}.$$