Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the projectivity of threefolds


Author: Zbigniew Jelonek
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
Published electronically: March 22, 2005
MathSciNet review: 2146196
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. Hartshorne, R, Ample Subvarieties of Algebraic Varieties, Springer-Verlag, 1986. MR 0282977 (44:211)
  • 2. Hartshorne, R, Algebraic Geometry, Springer-Verlag, 1997. MR 0463157 (57:3116)
  • 3. Hironaka, H, On the theory of birational blowing up, Thesis, Harvard, 1960.
  • 4. Kleiman, S, Toward a numerical theory of ampleness, Annals of Math. 84, 293-344, 1966. MR 0206009 (34:5834)
  • 5. Nagata, M, Imbedding of an abstract variety in a complete variety, J. Math. of Kyoto Univ. 2, 1-10, 1962-63.MR 0142549 (26:118)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14A10, 14A15

Retrieve articles in all journals with MSC (2000): 14A10, 14A15


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
Email: najelone@cyf-kr.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-05-07859-7
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.

American Mathematical Society