Tameness of Holomorphic Closure Dimension in a Semialgebraic Set
نویسنده
چکیده
Given a semianalytic set S in Cn and a point p ∈ S, there is a unique smallest complex-analytic germ Xp which contains Sp, called the holomorphic closure of Sp. We show that if S is semialgebraic then Xp is a Nash germ, for every p, and S admits a semialgebraic filtration by the holomorphic closure dimension. As a consequence, every semialgebraic subset of a complex vector space admits a semialgebraic stratification into CR manifolds.
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On the Holomorphic Closure Dimension of Real Analytic Sets
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