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ORIENTATIONS AND GEOMETRISATIONS OF COMPACT COMPLEX SURFACES

Published online by Cambridge University Press:  01 March 1997

D. KOTSCHICK
D. KOTSCHICK
Affiliation:
Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
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Abstract

Every complex manifold carries a canonical orientation, and it is natural to wonder when the underlying topological or smooth manifold carries a complex structure compatible with the other orientation. In [2], Beauville raised this question for compact complex surfaces. He noted that there are a lot of examples, like products of curves, or Hopf surfaces, where the underlying manifold admits an orientation-reversing selfdiffeomorphism. This implies that the signature is zero. Beauville asked if there are any examples of non-zero signature.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 145 - 149
Copyright
© The London Mathematical Society 1997

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