Real Algebraic and Analytic Geometry
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.
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