Lowest weights in cohomology of variations of Hodge structure (Q2894132)

Let \(X\) be a compact, Kähler irreducible complex analytic space and \(V\) a variation of Hodge structures of weight \(n\) on a Zariski open subset \(U\) of \(X\). When the local monodromy at infinity is quasi-unipotent, the intersection cohomology \(IH^k(X,V)\) carries a pure Hodge structure of weight \(k+n\), while the cohomology \(H^k(U,V)\) carries a mixed Hodge structure with weights at least \(k+n\).NEWLINENEWLINEThe authors show that the image of the natural morphism \(IH^k(X,V) \to H^k(U,V)\) is precisely the lowest weight part of this MHS, namely \(W_{k+n}H^k(U,V)\).