A formula to calculate the invariant $J$ of a quasi-homogeneous map germ

Abstract

In this work, we consider a quasi-homogeneous, corank 1, finitely determined map germ f from (C 2 , 0) to (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 (C 2 ). We present formulas to calculate m(f (D(f )) and J in terms of the weights and degrees of f .