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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- 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
- Email: email@example.com
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2539-2542
- MSC (2000): Primary 14A10, 14A15
- DOI: https://doi.org/10.1090/S0002-9939-05-07859-7
- MathSciNet review: 2146196