Convex foliations of degree 5 on the complex projective plane

We show that, up to automorphisms of P2 C, there are fourteen homogeneous convex foliations degree 5 on C. establish some properties the Fermat foliation Fd 0 d ≥ 2 and Hilbert modular F5H 5. As a consequence, we obtain that every reduced C is linearly conjugated one two F5 or H, which partial answer question posed in 2013 by D. Mar´in J. V. Pereira. end with conjectures about Camacho–Sad indices along line at infinity non radial singularities P2C.