Abstract

In the 1980s, there was significant progress in the $L^2$-theory of polarized variations of Hodge structure on higher dimensional varieties. In particular, according to the celebrated theorem of Cattani-Kaplan-Schmid and Kashiwara-Kawai, for a polarized variation of Hodge structure on the complement of a normal crossing hypersurface in a compact Kahler manifold, the $L^2$-cohomology and the intersection cohomology are isomorphic. Moreover, Kashiwara and Kawai announced that the induced Hodge filtration is described in terms of the filtered de Rham complex of the associated pure Hodge module. Recently, there has been a renewed interest in the subject. In this talk, we shall explain a generalization of the Kashiwara-Kawai theorem to the context of tame harmonic bundles.