Real Algebraic and Analytic Geometry |

On the holomorphic closure dimension of real analytic sets.

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Submission: 2011, July 2.

*Abstract:
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.

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