Baum-Bott indices for curves of singularities.

Let F be a holomorphic foliation on P by curves such that the components of its singular locus are curves C and points p . We compute the Baum-Bott indices BB ( F, C ) in terms of the main invariants of F and C . We also determine the sum of the BB ( F, p ) in terms of the same invariants.When φ corresponds to the determinant, the latter result generalizes, from special to all holomorphic foliations, a formula for the number of isolated singularities of F, counted with multiplicities. [ABSTRACT FROM AUTHOR]