0000000000703388
AUTHOR
J.j. Nuño-ballesteros
Double point curves for corank 2 map germs from C2 to C3
AbstractWe 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.
The doodle of a finitely determined map germ from R2 to R3
AbstractLet f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles.