Computing Camacho-Sad-Suwa indices of logarithmic vector fields relative to singular curves

Abstract Logarithmic vector fields along a singular curve and the Camacho-Sad-Suwa indices, generalizations of the Camacho-Sad index introduced by T. Suwa, are considered in the context of computational complex analysis. An effective algorithm is introduced for computing a basis of the module of germs of logarithmic vector fields along a given singular curve. A new method is described for computing the Camacho-Sad-Suwa indices. The keys of our approach are the use of local cohomology and Grothendieck local duality. Several examples are given for illustration.