1 1 O ct 2 00 6 UNITARY LOCAL SYSTEMS , MULTIPLIER IDEALS , AND POLYNOMIAL PERIODICITY OF HODGE NUMBERS

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quasi-projective case results of Green-Lazarsfeld and Simpson. As an application we show the polynomial periodicity of Hodge numbers h q,0 of congruence covers in any dimension, generalizing results of E. Hironaka and Sakuma. We derive a geometric characterization of finite abelian covers, which recovers the ones of Namba and Pardini. We use this to do some computations which appear in their published version only in some special cases.