Spectrum of Hyperplane Arrangements in Four Variables

Hodge spectrum is one of the most important invariants of hypersurface singularities and a hyperplane arrangement contains the simplest higher dimensional singular set. It is known that the Hodge spectra of hyperplane arrangements are combinatorial. Calculating the Hodge spectrum is a difficult task and combinatorial formulas exist for only a few cases. In this thesis the main result is the formula for reduced hyperplane arrangements in four variables.