abstract: Following the work of Beauville, Arapura, Delzant, Simpson a description of characteristic varieties of quasiprojective groups is given. This invariant measures the jumping numbers for the cohomology with respect to local system of coefficients. This description provides a number of obstructions (following ideas of Dimca, Papadima an Suciu) which can be applied to study the quasiprojectivity of Tits-Artin groups. It is a joint work with J.I. Cogolludo and D. Matei.