On the classification of complex multi-germs of corank one and codimension one - Houston, Kevin (Mathematica Scandinavica, 2005)
Corank one multi-germs f:(C^n,S)→ (C^p,0), n<p, of A_e-codimension one are classified. The mono-germs are given in an explicit normal form and the multi-germs are described in terms of augmentations, and concatenations of mono-germs and a special bi-germ.