Singularities of logarithmic foliations

A logarithmic 1-form on CPn can be written as GRAPHICS with (F) over cap (i)=(Pi(m)(0) F-j)/F-i for some homogeneous polynomials F-i of degree d(i) and constants lambda(i) is an element of C* such that Sigma lambda(i)d(i)=0. For general F-i, lambda(i), the singularities of omega consist of a schematic union of the codimension 2 subvarieties F-i=F-j=0 together with, possibly, finitely many isolated points. This is the case when all F-i are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities.