Tameness of Complex Dimension in a Real Analytic Set
نویسندگان
چکیده
منابع مشابه
Tameness of Complex Dimension in a Real Analytic Set
Given a real analytic set X in a complex manifold and a positive integer d, denote by Ad the set of points p in X at which there exists a germ of a complex analytic set of dimension d contained in X. It is proved that Ad is a closed semianalytic subset of X.
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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: Canadian Journal of Mathematics
سال: 2013
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2012-019-4