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2 results

  • Geometrically rational real conic bundles and very transitive actions

  • Part of
  • Jérémy Blanc, Frédéric Mangolte
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 1 / January 2011
    Published online by Cambridge University Press:
    13 September 2010, pp. 161-187
    Print publication:
    January 2011
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  • In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

  • Algebraic cycles and topology of real Enriques surfaces

  • FRÉDÉRIC MANGOLTE, JOOST VAN HAMEL
  • Journal:
    Compositio Mathematica / Volume 110 / Issue 2 / January 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 215-238
    Print publication:
    January 1998
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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 $Y$.