Monodromie d'une famille d'hypersurfaces

الأصل · EN

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.