On the analytic structure of double and triple points in the target of finite holomorphic multi-germs

We study the analytic structure of the double and triple point spaces M₂(f) and M₃(f) of finite multi-germs f (X,S)→(Cⁿ⁺¹,0), based on results of Mond and Pellikaan for the mono-germ case. We show that these spaces are Cohen-Macaulay, provided that certain dimensional conditions are satisfied, and give explicit expressions for their defining ideals in terms of those of their mono-germ branches.