Resumen de Convex foliations of degree 5 on the complex projective plane

Samir Bedrouni, David Marín Pérez

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