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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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On the Néron-Severi group of surfaces with many lines
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by Samuel Boissière and Alessandra Sarti PDF
Proc. Amer. Math. Soc. 136 (2008), 3861-3867 Request permission

Abstract:

For a binary quartic form $\phi$ without multiple factors, we classify the quartic $K3$ surfaces $\phi (x,y)=\phi (z,t)$ whose Néron-Severi group is (rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of prime degree without multiple factors, we prove that the Néron-Severi group of the surface $\phi (x,y)=\psi (z,t)$ is rationally generated by lines.
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Additional Information
  • Samuel Boissière
  • Affiliation: Laboratoire J.A. Dieudonné UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice, France
  • Email: samuel.boissiere@math.unice.fr
  • Alessandra Sarti
  • Affiliation: Johannes Gutenberg Universität Mainz, Institut für Mathematik, 55099 Mainz, Germany
  • MR Author ID: 651260
  • Email: sarti@mathematik.uni-mainz.de
  • Received by editor(s): January 22, 2007
  • Received by editor(s) in revised form: March 29, 2007, and October 9, 2007
  • Published electronically: June 3, 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. 136 (2008), 3861-3867
  • MSC (2000): Primary 14J28
  • DOI: https://doi.org/10.1090/S0002-9939-08-09475-6
  • MathSciNet review: 2425725