Real Algebraic and Analytic Geometry
Submission: 2011, July 2.
Given a real analytic (or, more generally, semianalytic) set R in a complex space, there is, for every point p of R, a unique smallest complex analytic germ at p that contains the germ of R at p. We call its complex dimension 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 proper analytic subset of R, and discuss the relationship between this dimension and the CR dimension of R.
Mathematics Subject Classification (2000): 32B20, 32V40.
Keywords and Phrases: real analytic sets, semianalytic sets, holomorphic closure dimension, complexification, Gabrielov regularity, CR dimension.
Full text, 12p.: dvi 69k, pdf 371k.