Some surfaces with maximal Picard number

Arnaud Beauville

doi:10.5802/jep.5

Arnaud Beauville ¹

¹ Laboratoire J.-A. Dieudonné, UMR 7351 du CNRS, Université de Nice Parc Valrose, F-06108 Nice cedex 2, France

Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 101-116.

Abstract
Résumé

For a smooth complex projective variety, the rank $ρ$ of the Néron-Severi group is bounded by the Hodge number $h^{1, 1}$ . Varieties with $ρ = h^{1, 1}$ 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.

Le rang $ρ$ 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 $ρ = h^{1, 1}$ 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.

Received: 2014-01-01
Accepted: 2014-05-15
Published online: 2014-08-26

MR Zbl

DOI: 10.5802/jep.5

Classification: 14J05, 14C22, 14C25
Keywords: Algebraic surfaces, Picard group, Picard number, curve correspondences, Jacobians
Mot clés : Surfaces algébriques, groupe de Picard, nombre de Picard, correspondances de courbes, jacobiennes

Author's affiliations:

Arnaud Beauville ¹

¹ Laboratoire J.-A. Dieudonné, UMR 7351 du CNRS, Université de Nice Parc Valrose, F-06108 Nice cedex 2, France

License:

CC-BY-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Arnaud Beauville. Some surfaces with maximal Picard number. Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 101-116. doi : 10.5802/jep.5. https://jep.centre-mersenne.org/articles/10.5802/jep.5/

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