TITLE: The fundamental group of a complex, quasi-affine variety
QUESTION [6 upvotes]: Can the fundamental group of a quasi-affine variety over $\mathbb{C}$ be a torsion group?

REPLY [6 votes]: A less interesting but personally checkable answer: consider $f : ({\mathbb C}^2 \setminus 0)/\{\pm 1\} \hookrightarrow {\mathbb C}^3$, $(x,y) \mapsto (x^2,xy,y^2)$. The image is the punctured quadric cone and obviously has fundamental group $\{\pm 1\}$.