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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:

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

Citing Articles

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[1]
Wojciech Kucharz
Mathematische Zeitschrift, 2016
[2]
János Kollár and Krzysztof Nowak
Mathematische Zeitschrift, 2015, Volume 279, Number 1-2, Page 85
[3]
Wojciech Kucharz
Archiv der Mathematik, 2014, Volume 102, Number 3, Page 257
[4]
Marcin Bilski, Wojciech Kucharz, Anna Valette, and Guillaume Valette
Mathematische Zeitschrift, 2013, Volume 275, Number 1-2, Page 403
[5]
Wojciech Kucharz
Topology and its Applications, 2013, Volume 160, Number 12, Page 1375
[6]
Wojciech Kucharz
Selecta Mathematica, 2011, Volume 17, Number 4, Page 855

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