Quasi-projectivity of normal varieties

Details Quasi-projectivity of normal varieties Quasi-projectivity of normal varieties

2011-12-05

arxiv.org/abs/1112.0975v2

Mathematics

Algebraic Geometry

6 pages, in english, presentation improved and reference added

Scientific paper

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 Wlodarczyk, using results of Boissiere, Gabber and Serman.

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