Resumen de Equisingularity of map germs from a surface to the plane

Juan José Nuño Ballesteros , B. Oréfice, Joao Nivaldo Tomazella

• Let (X, 0) be an ICIS of dimension 2 and let f:(X,0)\rightarrow (\mathbb C^2,0) be a map germ with an isolated instability. We look at the invariants that appear when X_s is a smoothing of (X, 0) and f_s:X_s\rightarrow B_\epsilon is a stabilization of f. We find relations between these invariants and also give necessary and sufficient conditions for a 1-parameter family to be Whitney equisingular. As an application, we show that a family (X_t,0) is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant with respect to t.