Degrees of spaces of holomorphic foliations of codimension one in Pn

Let F(d;n) be the parameter space of the family of holomorphic foliations of codimension one and degree d in Pn. Gomez-Mont and Lins-Neto have shown that the Zariski closure of the set of foliations defined by a differential 1-form of type aFdG−bGdF, where F, G denote co-prime homogeneous polynomials of degrees a,b is an irreducible component of F(a+b−2;n). Our main result gives a formula for the degree of this component for a=2, b odd.