Local structure of holomorphic foliation singularities (Q1127913)

The local behaviour of the leaves of a singular holomorphic foliation of a complex manifold is analyzed around the singularity. It is shown that certain integers classify the singular foliation germs. Maps from simpler classes to more complicated classes are constructed and it is shown that every foliation can be expressed in terms of simpler ones, under some mild assumptions. Examples are constructed to show the existence of germ classes corresponding to certain combination of integers.