Monodromie d'une famille d'hypersurfaces

Abstract

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.

29 pages, 8 figures

Cited by in corpus (2)

• Direct image of logarithmic complexes and infinitesimal invariants of cycles
• Monodromy of a family of hypersurfaces containing a given subvariety