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Publication Date:
July 2009
ISSN:
1615-7168
DOI:
10.1515/ADVGEOM.2009.024

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Advances in Geometry

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Rational maps in real algebraic geometry

Wojciech Kucharz1

1Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany and Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141, USA. Email: kucharz@math.unm.edu

Citation Information: Advances in Geometry. Volume 9, Issue 4, Pages 517–539, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/ADVGEOM.2009.024, July 2009

Publication History:
Received:
2007-09-12
Published Online:
2009-07-06

Abstract

The paper deals with rational maps between real algebraic sets. We are interested in the rational maps which extend to continuous maps defined on the entire source space. In particular, we prove that every continuous map between unit spheres is homotopic to a rational map of such a type. We also establish connections with algebraic cycles and vector bundles.

Key words.: Rational maps; real algebraic sets; vector bundles

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