Tameness of holomorphic closure dimension in a semialgebraic set
نویسندگان
چکیده
منابع مشابه
Tameness of Holomorphic Closure Dimension in a Semialgebraic Set
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 semial...
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Given a real analytic (or, more generally, semianalytic) set R in C (viewed as R), there is, for every p ∈ R̄, a unique smallest complex analytic germ Xp that contains the germ Rp. We call dimC Xp the holomorphic closure dimension of R at p. We show that the holomorphic closure dimension of an irreducible R is constant on the complement of a closed proper analytic subset of R, and discuss the re...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2012
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-012-0808-y