Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Algebraic cycles and algebraic models of smooth manifolds

Author: W. Kucharz
Journal: J. Algebraic Geom. 11 (2002), 101-127
Published electronically: November 16, 2001
MathSciNet review: 1865915
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Abstract | References | Additional Information

Abstract: By Tognoli’s theorem, any smooth compact manifold $M$ has an algebraic model, that is, there exists a nonsingular real algebraic set $X$ diffeomorphic to $M$. In fact, one can find an uncountable family of pairwise nonisomorphic algebraic models of $M$, assuming that $M$ has a positive dimension. In the present paper we are concerned with the group of homology classes on $X$ (with integer coefficients modulo $2$) that are represented by $d$-dimensional algebraic subsets of $X$. We investigate how this group varies as $X$ runs through the class of all algebraic models of $M$.

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Additional Information

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

Received by editor(s): March 24, 2000
Received by editor(s) in revised form: May 2, 2000
Published electronically: 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