Real Algebraic and Analytic Geometry
Submission: 2011, July 2.
Given a semianalytic set S in a complex space and a point p in the closure of S, there is a unique smallest complex analytic germ at p which contains the germ of S at p, called the holomorphic closure of S at p. We show that if S is semialgebraic then its holomorphic closure is a Nash germ, for every p, and S admits a semialgebraic filtration by the holomorphic closure dimension.
Mathematics Subject Classification (2000): 14P10, 32C07, 32V40, 32S45.
Keywords and Phrases: holomorphic closure, semialgebraic sets, CR manifolds.
Full text, 18p.: dvi 104k, pdf 373k.