On bifurcation points of a complex polynomial

Let $f: \mathbb{C} ^n \to \mathbb{C}$ be a polynomial of degree $d$. Assume that the set $\tilde{K}_\infty (f)=\{ y \in \mathbb{C} :$ there is a sequence $x_l\rightarrow\infty$ s.t. $f(x_l)\rightarrow y$ and $\Vert d f(x_l)\Vert\rightarrow 0\}$ is finite. We prove that the set $\tilde{K} (f)= K_0(f)\cup \tilde{K}_\infty (f)$ of generalized critical values of $f$ (hence in particular the set of bifurcation points of $f$) has at most $(d-1)^n$points. Moreover, $\char93 \tilde{K}_\infty (f)\le (d-1)^{n-1}.$ We also compute the set $\tilde{K} (f)$ effectively.