Real algebraic morphisms and Del Pezzo surfaces of degree 2 - Archive ouverte HAL
Article Dans Une Revue Journal of Algebraic Geometry Année : 2004

Real algebraic morphisms and Del Pezzo surfaces of degree 2

Frédéric Mangolte
Nuria Joglar-Prieto
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Résumé

Let X and Y be affine nonsingular real algebraic varieties. A general problem in Real Algebraic Geometry is to try to decide when a smooth map f : X -> Y can be approximated by regular maps in the space of smooth mappings from X to Y, equipped with the compact-open topology. In this paper we give a complete solution to this problem when the target space is the usual 2-dimensional sphere and the source space is a geometrically rational real algebraic surface. The approximation result for real algebraic surfaces rational over R is due to J. Bochnak and W. Kucharz. Here we give a detailed description of the more interesting case, namely a real Del Pezzo surfaces of degree 2.
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Dates et versions

hal-00001368 , version 1 (27-03-2004)

Identifiants

  • HAL Id : hal-00001368 , version 1

Citer

Frédéric Mangolte, Nuria Joglar-Prieto. Real algebraic morphisms and Del Pezzo surfaces of degree 2. Journal of Algebraic Geometry, 2004, 13, pp.269-285. ⟨hal-00001368⟩
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