On the Picard group of low-codimension subvarieties

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We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n − 2 inherit the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to results of Barth and Larsen). As an application, we give an affirmative answer (up to some mild natural numerical conditions) when the ambient space is a Grassmannian of lines (thus improving results of Barth, Van de Ven and Sommese) or a product of two projective spaces of the same dimension.
20 pages

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Algebraic Geometry, 14C22

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http://salesiana.dossiersoluciones.com/handle/123456789/104872

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511267
 http://arxiv.org/abs/math/0511267

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arXiv