Small codimension subvarieties in homogeneous spaces

Details Small codimension subvarieties in homogeneous spaces Small codimension subvarieties in homogeneous spaces

2010-05-04

arxiv.org/abs/1005.0468v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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 $X^2$ where $X$ is any isotropic grassmannian. We also deduce simple connectedness properties for subvarieties of $X$. Finally we prove transplanting theorems {\`a} 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.

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