The dynamics of holomorphic maps near curves of fixed points

Let M be a two-dimensional complex manifold and f : M -> M a holomorphic map. Let S subset of M be a curve made of fixed points of f, i.e. Fix(f) = S. We study the dynamics near S in case f acts as the identity on the normal bundle of the regular part of S. Besides results of local nature, we prove that if S is a globally and locally irreducible compact curve such that S . S < 0 then there exists a point P is an element of S and a holomorphic f-invariant curve with p on the boundary which is attracted by p under the action of f. These results are achieved introducing and studying a family of local holomorphic foliations related to f near S.