18.782 Arithmetic Geometry Lecture Note 16
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چکیده
Our goal for this lecture is to prove that morphisms of projective varieties are closed maps. In fact we will prove something stronger, that projective varieties are complete, a property that plays a role comparable to compactness in topology. For varieties, compactness as a topological space does not mean much because the Zariski topology is so coarse. Indeed, every subset of An (and hence of Pn) is compact (or quasicompact, if your definition of compactness includes Hausdorff).
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