Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group \Z

2007/02/20 by Nicolas Perrin, Perrin, Nicolas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Codimension #Combinatorics #FOS: Mathematics #Geometric and Algebraic Topology #Group (periodic table) #Homogeneous #Mathematical analysis #Mathematics #Physics #Picard group #Pure mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0702578

5 pages

arxiv created 2007/02/20 · openalex publication_date 2007/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth low-codimension subvariety X in a variety Y when Y is homogeneous. We prove that this method is strongly related to the signature σ_Y of the Poincare pairing on the middle cohomology of Y. We give under some topological assumptions a bound on the rank of Picard group Pic(X) in terms of σ_Y and remove these assumptions for grassmannians to generalise the main result of E. Arrondo and J. Caravantes.

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