Old and new examples of surfaces of general type with pg=0

Abstract. Surfaces of general type with geometric genus pg = 0, which can be given as Galois covering of the projective plane branched over an arrangement of lines with Galois group G = (Z/qZ) k, where k ≥ 2 and q is a prime number, are investigated. The classical Godeaux surface, Campedelli surfaces, Burniat surfaces, and a new surface X with K 2 X = 6 and (Z/3Z)3 ⊂ Tors(X) can be obtained as such coverings. It is proved that the group of automorphisms of a generic surface of the Campedelli type is isomorphic to (Z/2Z) 3. The irreducible components of the moduli space containing the Burniat surfaces are described. It is shown that the Burniat surface S with K2 S = 2 has the torsion group Tors(S) ≃ (Z/2Z) 3, (therefore, it belongs to the family of the Campedelli surfaces), i.e., the corresponding statement in the papers of C. Peters ”On certain examples of surfaces with pg = 0 ” in Nagoya Math. J. 66 (1977), and I. Dolgachev ”Algebraic surfaces with q = pg = 0 ” in Algebraic surfaces, Liguori, Napoli (1977),