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Tameness of Complex Dimension in a Real Analytic Set

  Published:2012-07-16
 Printed: Aug 2013
  • Janusz Adamus,
    Department of Mathematics, The University of Western Ontario, London, ON N6A 5B7
  • Serge Randriambololona,
    Department of Mathematics, The University of Western Ontario, London, ON N6A 5B7
  • Rasul Shafikov,
    Department of Mathematics, The University of Western Ontario, London, ON N6A 5B7
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Abstract

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 $X$.
Keywords: complex dimension, finite type, semianalytic set, tameness complex dimension, finite type, semianalytic set, tameness
MSC Classifications: 32B10, 32B20, 32C07, 32C25, 32V15, 32V40, 14P15 show english descriptions Germs of analytic sets, local parametrization
Semi-analytic sets and subanalytic sets [See also 14P15]
Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
Analytic subsets and submanifolds
CR manifolds as boundaries of domains
Real submanifolds in complex manifolds
Real analytic and semianalytic sets [See also 32B20, 32C05]
32B10 - Germs of analytic sets, local parametrization
32B20 - Semi-analytic sets and subanalytic sets [See also 14P15]
32C07 - Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
32C25 - Analytic subsets and submanifolds
32V15 - CR manifolds as boundaries of domains
32V40 - Real submanifolds in complex manifolds
14P15 - Real analytic and semianalytic sets [See also 32B20, 32C05]
 

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