On the holomorphic closure dimension of real analytic sets

Janusz Adamus; Rasul Shafikov

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arXiv · 0804.4511

On the holomorphic closure dimension of real analytic sets

Janusz Adamus·Rasul Shafikov

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Abstract

Given a real analytic (or, more generally, semianalytic) set R in the n-dimensional complex space, there is, for every point p in the closure of R, a unique smallest complex analytic germ X_p that contains the germ R_p. We call the complex dimension of X_p 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 relationship between this dimension and the CR dimension of R.

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Janusz Adamus, Rasul Shafikov. 2010-04-15. On the holomorphic closure dimension of real analytic sets. https://arxiv.org/abs/0804.4511

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