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

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

2007-02-20

arxiv.org/abs/math/0702578v1

Mathematics

Algebraic Geometry

5 pages

Scientific paper

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 \sigma_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 \sigma_Y and remove these assumptions for grassmannians to generalise the main result of E. Arrondo and J. Caravantes.

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