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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Threefolds containing Bordiga surfaces as ample divisors
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by Hidetoshi Maeda PDF
Proc. Amer. Math. Soc. 137 (2009), 1631-1639 Request permission

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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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
  • 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