Degrees of spaces of holomorphic foliations of codimension one in [formula omitted].

Let F ( d ; n ) be the parameter space of the family of holomorphic foliations of codimension one and degree d in P n . Gomez-Mont and Lins-Neto have shown that the Zariski closure of the set of foliations defined by a differential 1-form of type a F d G − b G d F , 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. [ABSTRACT FROM AUTHOR]