Abstract
We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth low-codimensional 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 Poincaré 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 recover the main result of E. Arrondo and J. Caravantes. To cite this article: N. Perrin, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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