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The first main purpose of this paper is to contribute to the existingknowledge about the complex projective surfaces $S$ of general type with$p_g(S) = 0$ and their moduli spaces, constructing 19 new families of suchsurfaces with hitherto unknown fundamental groups. We also provide a tablecontaining all the known such surfaces with K^2 <=7.  Our second main purpose is to describe in greater generality the fundamentalgroups of smooth projective varieties which occur as the minimal resolutions ofthe quotient of a product of curves by the action of a finite group.  We classify, in the two dimensional case, all the surfaces with q=p_g = 0obtained as the minimal resolution of such a quotient, having rational doublepoints as singularities. We show that all these surfaces give evidence to theBloch conjecture.

Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups