2004/03/09 by Ania Otwinowska, Otwinowska, Ania
Mathematics · #14C30 #14D05 #14D07 #Algebraic Geometry (math.AG) #FOS: Mathematics #General Topology (math.GN) #math.AG #math.GN #msc:14C30 #msc:14D05 #msc:14D07
paper · pdf · doi:10.48550/arxiv.math/0403151
29 pages, 8 figures
arxiv created 2004/03/09 · arxiv updated 2009/12/01
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.