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GAGA is short for Serre's 1956 paper "Géometrie Algébrique et Géométrie Analytique". The tag refers not only to that paper, but also to the way of thinking introduced by it.
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Stein Manifolds and Affine Varieties
Charlie, it is funny answering this way but here it is.
The criterion you are thinking about is a criterion that is relative to an embedding. It says that if $X$ is a quasi-affine complex normal var …