Double point curves for corank 2 map germs from [formula omitted] to [formula omitted

Abstract

We characterize finite determinacy of map germs f : ( C 2 , 0 ) → ( C 3 , 0 ) in terms of the Milnor number μ ( D ( f ) ) of the double point curve D ( f ) in ( C 2 , 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 f t : ( C 2 , 0 ) → ( C 3 , 0 ) is equivalent to the constancy of both μ ( D ( f t ) ) and μ ( f t ( C 2 ) ∩ H ) with respect to t, where H ⊂ C 3 is a generic plane.