Beauville surfaces without real structures

  • Ingrid Bauer
  • Fabrizio Catanese
  • Fritz Grunewald
Part of the Progress in Mathematics book series (PM, volume 235)

Summary

Inspired by a construction by Arnaud Beauville of a surface of general type with K2 = 8, pg = 0, the second author defined Beauville surfaces as the surfaces which are rigid, i.e., without nontrivial deformations, and which admit an unramified covering which is isomorphic to a product of curves of genus at least 2.

In this case the moduli space of surfaces homeomorphic to the given surface consists either of a unique real point, or of a pair of complex conjugate points corresponding to complex conjugate surfaces. It may also happen that a Beauville surface is biholomorphic to its complex conjugate surface, while failing to admit a real structure.

The first aim of this note is to provide series of concrete examples of the second situation, respectively of the third.

The second aim is to introduce a wider audience, in particular group theorists, to the problem of classification of such surfaces, especially with regard to the problem of existence of real structures on them.

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Copyright information

© Birkhäuser Boston 2005

Authors and Affiliations

  • Ingrid Bauer
    • 1
  • Fabrizio Catanese
    • 1
  • Fritz Grunewald
    • 2
  1. 1.Department of MathematicsUniversity of BayreuthBayreuthGermany
  2. 2.Mathematisches InstitutGermany

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