Fibers of the Baum-Bott map for foliations of degree two on ℙ.

The Baum-Bott map associates to a foliation the Baum-Bott indexes of their singularities. In this paper we study the fibers of the Baum-Bott map in the space of foliations of degree two on the projective plane ℙ. In the main result we prove that its generic fiber contains exactly 240 orbits of the natural action of Aut(ℙ) onthespace of foliations. [ABSTRACT FROM AUTHOR]