Quasi-projectivity of Normal Varieties
Olivier Benoist · International Mathematics Research Notices · 2012
We prove that a normal variety contains finitely many maximal quasi-projective open subvarieties. As a corollary, we obtain the following generalization of the Chevalley–Kleiman projectivity criterion: a normal variety is quasi-projective if and only if every finite subset is contained in an affine open subvariety. The proof builds on a strategy of Włodarczyk, using results of Boissière, Gabber, and Serman.