Some surfaces with maximal Picard number
Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 101-116.

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.

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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
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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