Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-21T06:07:54.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximation of Smooth Maps by Real Algebraic Morphisms

Published online by Cambridge University Press:  20 November 2018

Wojciech Kucharz  and
Kamil Rusek
Wojciech Kucharz
Affiliation:
University of New Mexico, Department of Mathematics and Statistics, Albuquerque, New Mexico 87131-1141, U.S.A., e-mail: kucharz@math.unm.edu
Kamil Rusek
Affiliation:
Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland, e-mail: rusek@im.uj.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let 𝔾 p,q(𝔽) be the Grassmann space of all q-dimensional 𝔽-vector subspaces of 𝔽 p, where 𝔽 stands for ℝ, ℂ or ℍ (the quaternions). Here 𝔾 p,q(𝔽) is regarded as a real algebraic variety. The paper investigates which C∞ maps from a nonsingular real algebraic variety X into 𝔾 p,q(𝔽) can be approximated, in the C ∞ compact-open topology, by real algebraic morphisms.

Keywords

14P0514P25

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 456 - 463
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Benedetti, R. and Tognoli, A., On real algebraic vector bundles. Bull. Sci. Math. 104 (1980), 89–112.Google Scholar
2. Bochnak, J., Coste, M. and Roy, M.-F., Géométrie Algébrique Réelle. Springer, New York and Berlin, 1987.Google Scholar
3. Bochnak, J., Buchner, M. and Kucharz, W., Vector bundles over real algebraic varieties. K-Theory 3 (1989), 271–298.Google Scholar
4. Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. of Math. (2) 79 (1964), 109–326.Google Scholar
5. Hirsch, M., Differential Topology. Springer, New York and Berlin, 1976.Google Scholar
6. Kucharz, W., Real algebraic morphisms into flag varieties. Boll. Un. Mat. Ital. A (7) 8 (1994), 345–352.Google Scholar
7. Tougeron, J.-Cl., Ideaux de Fonctions Differentiables. Springer, Berlin, Heidelberg, New York, 1972.Google Scholar