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ISSN 1088-6850(e) ISSN 0002-9947(p)

A four-dimensional deformation of a numerical Godeaux surface

Author(s): Caryn Werner
Journal: Trans. Amer. Math. Soc. 349 (1997), 1515-1525.
MSC (1991): Primary 14J29, 14J10.
MathSciNet review: 1407503
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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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