Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Real algebraic morphisms and Del Pezzo surfaces of degree $2$


Authors: Nuria Joglar-Prieto and Frédéric Mangolte
Journal: J. Algebraic Geom. 13 (2004), 269-285
DOI: https://doi.org/10.1090/S1056-3911-03-00344-8
Published electronically: September 24, 2003
MathSciNet review: 2047699
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Abstract | References | Additional Information

Abstract: 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 $f:X\rightarrow Y$ can be approximated by regular maps in the space of ${\mathcal{C}}^\infty$ mappings from $X$ to $Y$, equipped with the ${\mathcal{C}}^\infty$ topology.

In this paper we give a complete solution to this problem when the target space is the standard 2-dimensional sphere and the source space is a geometrically rational real algebraic surface. The approximation result for real algebraic surfaces rational over $\mathbb R$ is due to J. Bochnak and W. Kucharz.

Here we give a detailed description of the more interesting case, namely real Del Pezzo surfaces of degree 2.


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Additional Information

Nuria Joglar-Prieto
Affiliation: ITIS CES Felipe II, Universidad Complutense de Madrid, C/Capitán 39, 28300 Aranjuez Madrid, Spain
Email: njoglar@cesfelipesegundo.com

Frédéric Mangolte
Affiliation: Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac Cedex, France
Email: mangolte@univ-savoie.fr

DOI: https://doi.org/10.1090/S1056-3911-03-00344-8
Received by editor(s): October 1, 2001
Published electronically: September 24, 2003
Additional Notes: The first author was supported by a Marie Curie Postdoctoral Fellowship (number HPMF-CT-1999-00019) at the Department of Mathematics at the Vrije Universiteit, Amsterdam

American Mathematical Society