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Arnaud Beauville
Some surfaces with maximal Picard number
(Quelques surfaces dont le nombre de Picard est maximal)
Journal de l'École polytechnique — Mathématiques, 1 (2014), p. 101-116, doi: 10.5802/jep.5
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Class. Math.: 14J05, 14C22, 14C25
Keywords: Algebraic surfaces, Picard group, Picard number, curve correspondences, Jacobians

Résumé - Abstract

For a smooth complex projective variety, the rank $\rho $ of the Néron-Severi group is bounded by the Hodge number $h^{1,1}$. Varieties with $\rho =h^{1,1}$ have interesting properties, but are rather sparse, particularly in dimension $2$. We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.

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