This is page 2 of the notes.
I am confused how one obtains the "$\Bbb C$ picture" of curves of the form described
$$ y^2=x(x-a)(x-b)$$ and its projectivization $$y^2 z= x(x-az)(x-bz)$$
The picture is in $\Bbb R^3$... and I'm confused in the purpose of projectivization.
More generally,
how do people picture curves in $\Bbb P^2_{\Bbb C}$?