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 without multiple factors, we classify the quartic surfaces whose Néron-Severi group is (rationally) generated by lines. For generic binary forms , of prime degree without multiple factors, we prove that the Néron-Severi group of the surface 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

Email:
sarti@mathematik.uni-mainz.de

DOI:
https://doi.org/10.1090/S0002-9939-08-09475-6

Keywords:
N{\'e}ron-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.