L 2 and intersection cohomologies for a polarizable variation of Hodge structure (original) (raw)

We consider a polarized variation of Hodge structure (V, Vz, S, F) of weight k, over a complex manifold X 1-16]. Here V denotes a locally constant sheaf of finite dimensional complex vector spaces, V z a sheaf of lattices in V, and F a decreasing filtration of Ox | by locally free sheaves of Ox-modules F p. By assumption, the filtration F induces Hodge structure of weight k on the stalks of V, and satisfies the Riemann bilinear relations, as welt as the transversality relation, relative to the fiat bilinear form S. Typically variations of Hodge structure arise from the cohomology of the fibres in a family of smooth projective varieties.