Monodromie d'une famille d'hypersurfaces

Details Monodromie d'une famille d'hypersurfaces Monodromie d'une famille d'hypersurfaces

2004-03-09

arxiv.org/abs/math/0403151v1

Mathematics

Algebraic Geometry

29 pages, 8 figures

Scientific paper

I describe the monodromy of smooth hypersurfaces $X$ of high degree in a fixed smooth variety $Y$ containing a fixed subvariety $W$ of $Y$. The cohomology of $X$ in middle degree spanned by the pull-back of the cohomology of $Y$ and by the classes of the irreducible components of $W$ is monodromy invariant. I show that the monodromy representation on the orthogonal of those classes is irreducible. The proof is essentially topological. Difficulties arise from the fact that $W$ may have arbitrary singularities.

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