Search

A smooth algebraic surface S is said to be isogenous to a product of unmixed type if there exist two smooth curves C, F and a finite group G, acting faithfully on both C and F and freely on their product, so that S = (C × F)/G. In this article, we classify the surfaces of general type with pg = q = 1 which are isogenous to an unmixed product, assuming that the group G is abelian. It turns out that they belong to four families, that we call surfaces of type I, II, III, IV. The moduli spaces I, II, IV are irreducible, whereas III is the disjoint union of two irreducible components. In the last section we start the analysis of the case where G is not abelian, by constructing several examples. [ABSTRACT FROM AUTHOR]