In Liu's answer to this MO question there is a characterization of smooth affine varieties which are étale over affine space. I was wondering if one can give a similar characterization for projective varieties.
Let $X$ be a smooth projective variety of dimension $n$. When is $X$ étale over $\mathbb A^n$? How can one construct an étale map $X\to \mathbb A^n$?
I should maybe point out that I'm primarily interested in the case when the base field is $\mathbb C$.
Thank you for any help!