Monodromy of variations of Hodge structure
The \(k\)th primitive cohomology group \(H^k_{\text{prim}}(X)\) of a smooth projective variety \(X\) is known to carry a weight \(k\) polarized rational Hodge structure. For a family of those over a smooth connected base manifold \(S\), the cohomology groups glue together to a local system on \(S\). Such a local system is completely determined by its monodromy representation, i.e. the induced representation of \(\pi _1(S,s_0)\) on the \(k\)th cohomology group \(V\) of the fibre at \(s_0\). The authors present a survey of properties of the monodromy of local systems on quasi-projective varieties which underlie a variation of a Hodge structure. They also discuss a less widely known version of a Noether-Lefschetz-type theorem.
scientific article; zbMATH DE number 1901299