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Complex cycles on algebraic models of smooth manifolds

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Abstract

Every compact smooth manifold M is diffeomorphic to the set \({X(\mathbb{R})}\) of real points of a nonsingular projective real algebraic variety X, which is called an algebraic model of M. Each algebraic cycle of codimension k on the complex variety \({X_{\mathbb{C}}=X\times_{\mathbb{R}}\mathbb{C}}\) determines a cohomology class in \({H^{2k}(X(\mathbb{R});\mathbb{D})}\) , where \({\mathbb{D}}\) denotes \({\mathbb{Z}}\) or \({\mathbb{Q}}\) . We investigate the behavior of such cohomology classes as X runs through the class of algebraic models of M.

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  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, 87131, USA

    Wojciech Kucharz

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  1. Wojciech Kucharz
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Correspondence to Wojciech Kucharz.

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Kucharz, W. Complex cycles on algebraic models of smooth manifolds. Math. Ann. 346, 829–856 (2010). https://doi.org/10.1007/s00208-009-0413-x

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