Some surfaces with maximal Picard number

[Quelques surfaces dont le nombre de Picard est maximal]

Beauville, Arnaud

Journal de l'École polytechnique - Mathématiques, Tome 1 (2014), p. 101-116 / Harvested from Numdam

Résumé

Le rang $\rho $ du groupe de Néron-Severi d’une variété projective lisse complexe est borné par le nombre de Hodge $h^{1,1}$. Les variétés satisfaisant à $\rho =h^{1,1}$ ont des propriétés intéressantes, mais sont assez rares, particulièrement en dimension $2$. Dans cette note nous analysons un certain nombre d’exemples, notamment ceux construits à partir de courbes à jacobienne spéciale.

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.

Détail

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/jep.5
Classification:  14J05,  14C22,  14C25
Mots clés: Surfaces algébriques, groupe de Picard, nombre de Picard, correspondances de courbes, jacobiennes

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