2010/05/04 by Nicolas Perrin, Perrin, Nicolas
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1005.0468
20 pages
arxiv created 2010/05/04 · arxiv updated 2010/05/05
We prove Bertini type theorems for the inverse image, under a proper morphism, of any Schubert variety in an homogeneous space. Using generalisations of Deligne's trick, we deduce connectedness results for the inverse image of the diagonal in X2 where X is any isotropic grassmannian. We also deduce simple connectedness properties for subvarieties of X. Finally we prove transplanting theorems à la Barth-Larsen for the Picard group of any isotropic grassmannian of lines and for the Neron-Severi group of some adjoint and coadjoint homogeneous spaces.