Examples of quasi-projective varieties that are not (topologically) quasi-affine I'm trying to think of a quasi-projective variety that is not isomorphic to a quasi-affine one. I image that it must be $Y \subseteq \mathbb{P}^n$ of at least $n \geq 3$, and maybe $\operatorname{dim} Y \geq 2$ as well. I am also interested in finding a low (co)dimensional example of a quasi-projective that is not homeomorphic to a quasi-affine. 

I think $\mathbb{P}^2 - pt$ is an example, but I would have to think longer about why this can't be quasi-affine. 
(I think you can argue that if it were quasi-affine, it would have global functions, but if that were the case, you would be able to find global functions on $\mathbb{P}^2$, which can't be. Hartog's extension theorem works over $\mathbb{C}$.)
