## Threefolds containing Bordiga surfaces as ample divisors

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- by Hidetoshi Maeda
- Proc. Amer. Math. Soc.
**137**(2009), 1631-1639 - DOI: https://doi.org/10.1090/S0002-9939-08-09752-9
- Published electronically: November 26, 2008
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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 $\mathcal {E}$.## References

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## Bibliographic 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
- 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2470821