The moduli space of surfaces of general type with fixed numerical invariants is an intricate object. For most choices of invariants it has many irreducible components and it is not pure dimensional. Despite the fact that the moduli space of surfaces of general type with geometric genus zero is far from an exception to this idea, for historical reasons, there is a great deal of interest in it. The best understood cases are those of numerical Godeaux surfaces, for which K^2=1, and numerical Campedelli surfaces, for which K^2=2. In both cases, there exists a classification of the connected components of the corresponding two moduli spaces based on the algebraic fundamental group. Indeed, the algebraic fundamental groups of numerical Godeaux surfaces have order less than or equal to 5 and are all cyclic, whereas those of numerical Campedelli surfaces have order less than or equal to 9 and all but the dihedral of order 8 and the symmetric group of order 6 occur. Since there are surfaces with geometric genus zero, K^2=4 and infinite algebraic fundamental group, the case K^2=3 remains the last one in which a classification of components based on the algebraic fundamental group may be achieved. Although it has not been proved there is a bound on the order of the algebraic fundamental of these surfaces, it is believed that such a bound exists and that 16 comes close to it.

In this talk we shall describe a new component of the moduli space of surfaces of general type with geometric genus zero and K^2=3 with algebraic fundamental group a semi-direct product of two cyclic groups of order 4. This is joint work with G. Bini, F. Favale and R. Pignatelli.