A pr 2 00 4 OLD AND NEW EXAMPLES OF SURFACES OF GENERAL TYPE WITH p g = 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), 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 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). The irreducible components of the moduli space containing the Burniat surfaces are described. It is shown that the Burniat surface S with K S = 2 has the torsion group Tors (S) ≃ (Z/2Z), (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), and in the book of W. Barth, C. Peters, A. Van de Ven ”Compact complex surfaces”, p. 237, about the torsion group of the Burniat surface S with K S = 2 is not correct.

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Cite this paper

@inproceedings{Kulikov2004AP2, title={A pr 2 00 4 OLD AND NEW EXAMPLES OF SURFACES OF GENERAL TYPE WITH p g = 0}, author={Vik . S . Kulikov}, year={2004} }