Tameness of holomorphic closure dimension in a semialgebraic set

Details Tameness of holomorphic closure dimension in a semialgebraic set Tameness of holomorphic closure dimension in a semialgebraic set

2011-05-11

arxiv.org/abs/1105.2310v2

Mathematics

Complex Variables

18 pages

Scientific paper

Given a semianalytic set S in a complex space and a point p in S, there is a unique smallest complex-analytic germ at p which contains the germ of S, called the holomorphic closure of S at p. We show that if S is semialgebraic then its holomorphic closure 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 satisfying a strong version of the condition of the frontier.

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