Residue-type indices and holomorphic foliations

Arturo Fernández-Pérez, Rogério Mol

Published 2017-03-03Version 1

We investigate residue-type indices for germs of holomorphic foliations in the plane and characterize second type foliations - those not containing tangent saddle-nodes in the reduction of singularities - by an expression involving the Baum-Bott, variation and polar excess indices. These local results are applied in the study of logarithmic foliations on compact complex surfaces.