Consider the projective space ${\mathbb P}^{n}_{k}$ with field $k$. We can naturally give this the Zariski topology.
Question: What are the (proper) compact sets in this space?
Motivation: I wanted nice examples of spaces and their corresponding compact sets; usually my spaces are Hausdorff and my go-to topology for non-Hausdorff-ness is the Zariski topology. I wasn't really able to find any proper compact sets which makes me think I'm doing something wrong here.