Journal of Algebraic Geometry

Author(s): W. Kucharz
Journal: J. Algebraic Geom. 11 (2002), 101-127.
Posted: November 16, 2001
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Abstract: By Tognoli's theorem, any smooth compact manifold

has an algebraic model, that is, there exists a nonsingular real algebraic set

diffeomorphic to

. In fact, one can find an uncountable family of pairwise nonisomorphic algebraic models of

, assuming that

has a positive dimension. In the present paper we are concerned with the group of homology classes on

(with integer coefficients modulo

) that are represented by

-dimensional algebraic subsets of

. We investigate how this group varies as

runs through the class of all algebraic models of

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W. Kucharz
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141
Email: kucharz@math.unm.edu

PII: S 1056-3911(01)00292-2
Received by editor(s): March 24, 2000
Received by editor(s) in revised form: May 2, 2000
Posted: November 16, 2001
Additional Notes: The author was partially supported by NSF Grant DMS-9503138. The paper was completed at the Max-Planck-Institut für Mathematik in Bonn, whose support and hospitality is gratefully acknowledged

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