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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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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: https://doi.org/10.1515/ADVGEOM.2009.024, July 2009

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

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