From [a post](http://mathoverflow.net/questions/7374/the-jouanolou-trick/7602#7602) to [The Jouanolou trick](http://mathoverflow.net/questions/7374/the-jouanolou-trick/):

> Are there examples of a **topologically trivial** (contractible) **complex algebraic varieties** other then affine lines? If yes, are all of them necessarily affine?

This looks like some kind of comparison between Zariski cohomology and complex cohomology.