Beauville surfaces without real structures
- Ingrid BauerAffiliated withDepartment of Mathematics, University of Bayreuth
- , Fabrizio CataneseAffiliated withDepartment of Mathematics, University of Bayreuth
- , Fritz GrunewaldAffiliated withMathematisches Institut
Inspired by a construction by Arnaud Beauville of a surface of general type with K 2 = 8, p g = 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.
- Beauville surfaces without real structures
- Book Title
- Geometric Methods in Algebra and Number Theory
- pp 1-42
- Print ISBN
- Online ISBN
- Series Title
- Progress in Mathematics
- Series Volume
- Birkhäuser Boston
- Copyright Holder
- Birkhäuser Boston
- Additional Links
- Industry Sectors
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- Editor Affiliations
- 1. Department of Mathematics Courant Institute of Mathematical Sciences, New York University
- 2. Department of Mathematics, Princeton University
- Author Affiliations
- 3. Department of Mathematics, University of Bayreuth, D-95440, Bayreuth, Germany
- 4. Mathematisches Institut, Universitätsstrasse 1, D-40225, Germany
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