On the Picard group of low-codimension subvarieties

2005/11/10 by Enrique Arrondo, Arrondo, Enrique, Jorge Caravantes +1
Computer Science · Mathematics · #14C22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #math.AG #msc:14C22

paper · pdf · doi:10.48550/arxiv.math/0511267

20 pages

openalex publication_date 2005/11/10 · arxiv created 2006/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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