Real Algebraic and Analytic Geometry

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179. W. Kucharz, K. Kurdyka:
Algebraicity of global real analytic hypersurfaces.

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Submission: 2005, November 7.

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.

Mathematics Subject Classification (2000): 14Pxx,14F05, 14F25, 32B05.

Full text, 14p.: dvi 45k, ps.gz 114k, pdf 150k.

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