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On the projectivity of threefolds
Author(s):
Zbigniew
Jelonek
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2539-2542.
MSC (2000):
Primary 14A10, 14A15
Posted:
March 22, 2005
MathSciNet review:
2146196
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Abstract:
Let  be a smooth complete three-dimensional algebraic variety (defined over an algebraically closed field  ). We show that  is projective if it contains a divisor which is positive on the cone of effective curves.
References:
-
- 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)
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Additional Information:
Zbigniew
Jelonek
Affiliation:
Instytut Matematyczny, Polska Akademia Nauk, Sw. 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:
10.1090/S0002-9939-05-07859-7
PII:
S 0002-9939(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
Posted:
March 22, 2005
Additional Notes:
The author was partially supported by the KBN grant number 2PO3A 01722
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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