Algebraicity of Global Real Analytic Hypersurfaces |
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Authors: | Wojciech Kucharz Krzysztof Kurdyka |
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Institution: | (1) Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141, USA;(2) Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France |
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Abstract: | Let X be an algebraic manifold without compact component and let V be a compact coherent analytic hypersurface in X, with finite singular set. We prove that V is diffeotopic (in X) to an algebraic hypersurface in X if and only if the homology class represented by V is algebraic and singularities are locally analytically equivalent to Nash singularities. This allows us to construct algebraic hypersurfaces in X with prescribed Nash singularities. |
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Keywords: | Algebraic cycles Real analytic hypersurfaces |
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