Tameness of Complex Dimension in a Real Analytic Set

Adamus, Janusz ; Randriambololona, Serge ; Shafikov, Rasul

Canadian journal of mathematics, Tome 65 (2013) no. 4, pp. 721-739

Résumé

Given a real analytic set $X$ in a complex manifold and a positive integer $d$ , denote by ${{\mathcal{A}}^{d}}$ the set of points $p$ in $X$ at which there exists a germ of a complex analytic set of dimension $d$ contained in $X$ . It is proved that ${{\mathcal{A}}^{d}}$ is a closed semianalytic subset of $X$ .

Détail

DOI : 10.4153/CJM-2012-019-4

Mots-clés : 32B10, 32B20, 32C07, 32C25, 32V15, 32V40, 32V40, complex dimension, finite type, semianalytic set, tameness

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