The coherence of complemented ideals in the space of real analytic functions |
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Authors: | Pawe? Domański Dietmar Vogt |
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Institution: | 1. Faculty of Mathematics and Computer Science, A. Mickiewicz University Poznań and Institute of Mathematics of the Polish Academy of Sciences (Poznan branch), Umultowska 87, 61-614, Poznan, Poland 2. Bergische Universit?t Wuppertal, FB Mathematik, Gau?str. 20, 42097, Wuppertal, Germany
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Abstract: | We characterize when an ideal of the algebra ${A(\mathbb{R}^d)}We characterize when an ideal of the algebra
A(\mathbbRd){A(\mathbb{R}^d)} of real analytic functions on
\mathbbRd{\mathbb{R}^d} which is determined by the germ at
\mathbb Rd{\mathbb {R}^d} of a complex analytic set V is complemented under the assumption that either V is homogeneous or
V?\mathbbRd{V\cap \mathbb{R}^d} is compact. The characterization is given in terms of properties of the real singularities of V. In particular, for an arbitrary complex analytic variety V complementedness of the corresponding ideal in
A(\mathbbRd){A(\mathbb{R}^d)} implies that the real part of V is coherent. We also describe the closed ideals of
A(\mathbbRd){A(\mathbb{R}^d)} as sections of coherent sheaves. |
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