Double point curves for corank 2 map germs from C2 to C3

We characterize finite determinacy of map germs f:(C2,0)→(C3,0) in terms of the Milnor number μ(D(f)) of the double point curve D(f) in (C2,0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs ft:(C2,0)→(C3,0) is equivalent to the constancy of both μ(D(ft)) and μ(ft(C2)∩H) with respect to t, where H⊂C3 is a generic plane.