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Algebraic cycles and topology of real Enriques surfaces

Published online by Cambridge University Press:  04 December 2007

FRÉDÉRIC MANGOLTE  and
JOOST VAN HAMEL
FRÉDÉRIC MANGOLTE
Affiliation:
Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac Cedex, France; e-mail: mangolte@math.univ-savoie.fr
JOOST VAN HAMEL
Affiliation:
Faculteit der Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands; e-mail: vanhamel@math.ruu.nl
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Abstract

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For a real Enriques surface $Y$ we prove that every homology class in $H_1(Y(R), Z/2)$ can be represented by a real algebraic curve if and only if all connected components of $Y(R)$ are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface $Y$.

Keywords

Algebraic cyclesreal algebraic surfacesEnriques surfacesGalois-MaximalityBrauer group
Type
Research Article
Information
Compositio Mathematica , Volume 110 , Issue 2 , January 1998 , pp. 215 - 238
Copyright
© 1998 Kluwer Academic Publishers