AbstractsMathematics

In this thesis we study varieties isogenous to a product and product quotient varieties with canonical singularities in dimension three. A variety X isogenous to a product of curves is a quotient of a product of compact Riemann surfaces of genus at least two by the free action of a finite group: X=ig(C1  ×  …  ×  Cnig)/G. Since Catanese introduced these objects they turned out to be very useful to find new and interesting examples of varieties of general type. Especially the surface case has been studied extensively. We are interested in the systematic construction and classification of these varieties in dimension three. Our first main result is the full classification of threefolds isogenous to a product with χ(