Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group Z
نویسنده
چکیده
We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth lowcodimension subvariety X in a variety Y when Y is homogeneous. We prove that this method is strongly related to the signature σY 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 σY and remove these assumptions for grassmannians to recover the main result of E. Arrondo and J. Caravantes.
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تاریخ انتشار 2007