Abstract
Given a real analytic (or, more generally, semianalytic) set R in Cn (viewed as R2n), there is, for every p ∈ R, 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 we discuss the relationship between this dimension and the CR dimension of R.
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