Quasi-projectivity of normal varieties

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02353612
Contributor : Olivier Benoist <>
Submitted on : Thursday, November 7, 2019 - 1:32:51 PM
Last modification on : Tuesday, November 12, 2019 - 10:50:04 AM

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Olivier Benoist. Quasi-projectivity of normal varieties. International Mathematics Research Notices, Oxford University Press (OUP), 2013, 2013 (17), pp.3878-3885. ⟨10.1093/imrn/rns163⟩. ⟨hal-02353612⟩

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