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COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES

Published online by Cambridge University Press:  19 December 2014

WOJCIECH KUCHARZ
WOJCIECH KUCHARZ*
Affiliation:
Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Profesora Łojasiewicza 6, 30-348 Kraków, Poland E-mail: Wojciech.Kucharz@im.uj.edu.pl
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Abstract

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Let Y be a compact nonsingular real algebraic variety of positive dimension. Then one can find a compact connected nonsingular real algebraic variety X, which admits a continuous map into Y that is not homotopic to any regular map. It is hard to determine the minimum dimension of such a variety X. In this paper, new upper bounds for dim X are obtained. The main role in the constructions is played by complex algebraic cycles on Y.

MSC classification

Primary: 14P05: Real algebraic sets
Secondary: 14P25: Topology of real algebraic varieties
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 343 - 347
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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