2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169936In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an arbitrary divisor in a smooth projective complex variety. The second result is an application of the first. We give a combinatorial formula for the spectrum of a hyperplane arrangement. M. Saito recently proved that the spectrum of a hyperplane arrangement depends only on combinatorics. However, a combinatorial formula was missing. The formula is achieved by a different method.v2: added references to Prof. Libgober's workAlgebraic Geometry14B05, 32S35, 32S22text