Why the complex projective space $P^n$ and its irreducible Zariski closed subsets are examples of non-affine varieties?
I read this on Siddarth Kannan - An informal introduction to blow-ups, page 1.
2026-03-29 21:58:14.1774821494
Why projective varieties are non affine varieties
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If $X$ is an affine variety, $X = {\rm Spec} A$, then $A$ is the ring of global sections of the structure sheaf ${\mathcal O}_X$. But for a projective variety $X$, any global section of ${\mathcal O}_X$ is a constant function. The ring of global sections is just the ground field, and its spectrum is a point, not $X$.