Real Algebraic and Analytic Geometry |

Algebraicity of global real analytic hypersurfaces.

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Submission: 2005, November 7.

*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.*

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

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