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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A four-dimensional deformation of
a numerical Godeaux surface


Author: Caryn Werner
Journal: Trans. Amer. Math. Soc. 349 (1997), 1515-1525
MSC (1991): Primary 14J29, 14J10.
DOI: https://doi.org/10.1090/S0002-9947-97-01892-8
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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Additional Information

Caryn Werner
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: cwerner@math.lsa.umich.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01892-8
Received by editor(s): September 10, 1995
Article copyright: © Copyright 1997 American Mathematical Society

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