Recognition and Implementation of Contact Simple Map Germs from (ℂ2, 0) → (ℂ2, 0)

Abstract

The classification of contact simple map germs from (C2,0)→(C2,0) was given by Dimca and Gibson. In this article, we give a useful criteria to recognize this classification of contact simple map germs of holomorphic mappings with finite codimension. The recognition is based on the computation of explicit numerical invariants. By using this characterization, we implement an algorithm to compute the type of the contact simple map germs without computing the normal form and also give its implementation in the computer algebra system Singular.