I have a hard time going between points and lines in projective space. For example, if I want to consider the line $x = 0,$ then I know this corresponds to the point $$[0 : y : z] = [0 : 1 : z/y] \rightarrow [0: 1 : 0]$$ as $y \rightarrow \infty.$ I know this is the line at infinity, but I don't know what this looks like as an actual line, if that makes any sense. Can anyone help me visualize what a line looks like in $\mathbb{C}\mathbb{P}^2?$
2026-03-27 00:09:31.1774570171
What does a line look like in $\mathbb{C}\mathbb{P}^2?$
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