A four-dimensional deformation of a numerical Godeaux surface

Werner, Caryn

doi:10.1090/S0002-9947-97-01892-8

A four-dimensional deformation of a numerical Godeaux surface
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by Caryn Werner

Trans. Amer. Math. Soc. 349 (1997), 1515-1525

DOI: https://doi.org/10.1090/S0002-9947-97-01892-8

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Abstract:

A numerical Godeaux surface is a surface of general type with invariants $p_g =q =0$ and $K^2 =1$. In this paper the moduli space of a numerical Godeaux surface with order two torsion is computed to be eight-dimensional; whether or not the moduli space of such a surface is irreducible is still unknown. The surface in this paper is constructed as one member of a four parameter family of double planes. There is a natural involution on the surface, inherited from the double plane construction, which acts on the moduli space. We show that the invariant subspace is four-dimensional and coincides with the family of double planes.

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