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On the Néron-Severi group of surfaces with many lines

Authors: Samuel Boissière and Alessandra Sarti
Journal: Proc. Amer. Math. Soc. 136 (2008), 3861-3867
MSC (2000): Primary 14J28
Published electronically: June 3, 2008
MathSciNet review: 2425725
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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

Alessandra Sarti
Affiliation: Johannes Gutenberg Universität Mainz, Institut für Mathematik, 55099 Mainz, Germany
MR Author ID: 651260

Keywords: Néron-Severi group, Picard number, lines on surfaces
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.