Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2011, July 2.

Abstract:
Given a real analytic set X in a complex manifold and a positive integer d, denote by A(X,d) the set of points p in X for which there exists a germ at p of a complex analytic set of dimension at least d contained in the germ of X at p. It is proved that the A(X,d) are closed semianalytic subsets of X. If, moreover, X is real algebraic, then the A(X,d) are semialgebraic. .

Mathematics Subject Classification (2000): 32B10, 32B20, 32C07, 32C25, 32V15, 32V40, 14P15.

Keywords and Phrases: real analytic sets, semianalytic sets, Segre varieties.

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