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Proceedings of the American Mathematical Society

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On the projectivity of threefolds

Author: Zbigniew Jelonek
Journal: Proc. Amer. Math. Soc. 133 (2005), 2539-2542
MSC (2000): Primary 14A10, 14A15
Published electronically: March 22, 2005
MathSciNet review: 2146196
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Abstract: Let $X$ be a smooth complete three-dimensional algebraic variety (defined over an algebraically closed field $k$). We show that $X$ is projective if it contains a divisor which is positive on the cone of effective curves.

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Additional Information

Zbigniew Jelonek
Affiliation: Instytut Matematyczny, Polska Akademia Nauk, Św. Tomasza 30, 31-027 Kraków, Poland
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906

Keywords: Projectivity, threefold, maximal quasi-projective subsets
Received by editor(s): November 8, 2003
Received by editor(s) in revised form: May 17, 2004
Published electronically: March 22, 2005
Additional Notes: The author was partially supported by the KBN grant number 2PO3A 01722
Communicated by: Michael Stillman
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.