Divisors and Picard Group

Question

I was wondering if there exists any relation between the group of Weil divisors (and the Picard´s group) of an affine variety, and the group of Weild divisors (and the Picard´s group) of it´s projective closure.

Answer 1

If $X$ is a variety open in a variety $Y$, there is always a map from the group of Weil divisors on $Y$ to that of $X$ and the same for Picard group. The first map is onto, the second map may not be.