On the Picard Group of Low-codimension Subvarieties



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Arrondo Esteban, Enrique and Caravantes, Jorge (2009) On the Picard Group of Low-codimension Subvarieties. Indiana University Mathematics Journal, 58 (3). pp. 1023-1042. ISSN 0022-2518

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Official URL: http://arxiv.org/pdf/math/0511267.pdf


We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n - 2 inherits 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 (LIP 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.

Item Type:Article
Uncontrolled Keywords:Projective spaces; Manifolds; Low codimension; Picard group
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14769
Deposited On:18 Apr 2012 08:26
Last Modified:03 Oct 2018 11:52

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