Suppose $f: \mathbb{C}^n \to \mathbb{C}^n$ is a proper polynomial mapping and $\gamma: [0,1] \to \mathbb{C}^n$ is a continuous path. Further, suppose $z_0 \in \C^n$ satisfies $f(z_0)=\gamma(0)$. Does there exist a (not necessarily unique) lift of $\gamma$ under $f$ based at $z_0$? Is there a published reference for this fact?

Suppose $f: \mathbb{C}^n \to \mathbb{C}^n$ is a proper polynomial mapping and $\gamma: [0,1] \to \mathbb{C}^n$ is a continuous path. Further, suppose $z_0 \in \mathbb{C}^n$ satisfies $f(z_0)=\gamma(0)$. Does there exist a (not necessarily unique) lift of $\gamma$ under $f$ based at $z_0$? Is there a published reference for this fact?