On invariants of a map germ from n-space to 2n-space

We consider \(\mathcal{A}\)-finite map germs \(f\) from \((\mathbb{C}^n,0)\) to \((\mathbb{C}^{2n},0)\). First, we show that the number of double points that appears in a stabilization of \(f\), denoted by \(d(f)\), can be calculated as the length of the local ring of the double point set \(D^2(f)\) of \(f\), given by the Mond's ideal. In the case where \(n\leq 3\) and \(f\) is quasihomogeneous, we also present a formula to calculate \(d(f)\) in terms of the weights and degrees of \(f\). Finally, we consider an unfolding \(F(x,t) = (f_t(x),t)\) of \(f\) and we find a set of invariants whose constancy in the family \(f_t\) is equivalent to the Whitney equisingularity of \(F\). As an application, we present a formula to calculate the Euler obstruction of the image of \(f\).