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Bulletin of the London Mathematical Society 2001 33(1):32-40; doi:10.1112/blms/33.1.32
© 2001 by London Mathematical Society
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© London Mathematical Society

Complexification of Real Algebraic Varieties and Vanishing of Homology Classes

J. Bochnak and W. Kucharz

Department of Mathematics, Vrije Universiteit De boelelaan 1081 A, 1081 HV, Amsterdam, The Netherlands; e-mail: bochnak{at}cs.vu.nl
Department of Mathematics, University of New Mexico Albuquerque, NM 87131, USA; e-mail: kucharz{at}math.unm.edu

Received 7 February 1999. Revision received 5 September 1999.

Let X be a nonsingular real algebraic variety, and let X(C) be its nonsingular projective complexification. We study the following question: when does the homology class represented by X in the homology group of X(C) vanish? An application concerning the structure of the set of regular mappings is given.

Both authors were partially supported by NATO Collaborative Research Grants Programme CRG 960011.

The second author was partially supported by NSF Grant DMS-9503138.


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