On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space

Abstract

In this work, we consider a quasi-homogeneous, corank 1, finitely determined map germ f from $$(\mathbb {C}^2,0)$$ to $$(\mathbb {C}^3,0)$$ . We consider the invariants m(f(D(f))) and J, where m(f(D(f))) denotes the multiplicity of the image of the double point curve D(f) of f and J denotes the number of tacnodes that appears in a stabilization of the transversal slice curve of $$f(\mathbb {C}^2)$$ . We present formulas to calculate m(f(D(f))) and J in terms of the weights and degrees of f.