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Proceedings of the American Mathematical Society

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

 
 

 

Threefolds containing Bordiga surfaces as ample divisors


Author: Hidetoshi Maeda
Journal: Proc. Amer. Math. Soc. 137 (2009), 1631-1639
MSC (2000): Primary 14J25; Secondary 14J30, 14J60
DOI: https://doi.org/10.1090/S0002-9939-08-09752-9
Published electronically: November 26, 2008
MathSciNet review: 2470821
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Abstract: Let $L$ be an ample line bundle on a smooth complex projective variety $X$ of dimension three such that there exists a smooth member $Z$ of $\vert L\vert$. When the restriction $L_{Z}$ of $L$ to $Z$ is very ample and $(Z,L_{Z})$ is a Bordiga surface, it is proved that there exists an ample vector bundle $\mathcal {E}$ of rank two on $\mathbb {P}^{2}$ with $c_{1}(\mathcal {E}) = 4$ and $3 \leq c_{2}(\mathcal {E}) \leq 10$ such that $(X,L) = (\mathbb {P}_{\mathbb {P}^{2}}(\mathcal {E}),H(\mathcal {E}))$, where $H(\mathcal {E})$ is the tautological line bundle on the projective space bundle $\mathbb {P}_{\mathbb {P}^{2}}(\mathcal {E})$ associated to $\mathcal {E}$.


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Additional Information

Hidetoshi Maeda
Affiliation: Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
Email: maeda@variety.sci.waseda.ac.jp

Keywords: Ample line bundle, Bordiga surface
Received by editor(s): November 23, 2007
Received by editor(s) in revised form: July 16, 2008
Published electronically: November 26, 2008
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.