Abstract
In this chapter we shall study, first locally and then globally, the complexification of a real analytic space (variety). The main results for the local models, which will be exposed in the first two paragraphs, are due to H. Cartan [2]. The existence of a complexification for a real analytic manifold was proved by F. Bruhat and H. Whitney [1], H.B. Shutrick [9], A. Haefliger [5] and, in the compact case, by C.B. Morrey [8]. The extension to real analytic spaces, which had been announced by H. Hironaka [6], was given by A. Tognoli [10].
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Bibliography
F. BRUHAT, H. WHITNEY, Quelques proprietés fondamentales des ensembles analytiques réels, Comm. Math. Helv. 36 2 (1959), 132–160.
H. CARTAN, Variétés analytiques rée1les et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77–99.
H. GRAUERT, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. Math. 68 (1958), 460–472.
H. GRAUERT, R. REMMERT, Theory of Stein Spaces, Grundl. 236, Springer-Verlag, Berlin 1979.
A. HAEFLIGER, Structures feuilletées et cohomologie à valeurs dans un faisceau de groupoides, Comm. Math. Helv. 32 (1958), 248–329.
H. HIRONAKA, The resolution of singularities of an algebraic variety, Ann. Math. 79 (1964), 109–326.
B. MALGRANGE, Sur les fonctions différentiables et les ensembles analytiques, Bull. Soc. Math. France 91 (1963), 113–127.
C.B. MORREY, The analytic embedding of abstract real-analytic manifolds, Ann. Math. 68 (1958), 159–201.
H.B. SHUTRICK, Complex extension, Quart. J. of Mech. and Appl. Math. 9 (1958), 189–201.
A. TOGNOLI, Proprietà globali degli spazi analitici reali, Ann. Mat. Pura e Appl. (4) 75 (1967), 143–218.
A. TOGNOLI, Introduzione alla teoria degli spazi analitici reali, Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e loro Applicazioni n. 21, Accademia Nazionale dei Lincei, Roma 1976.
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© 1986 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Guaraldo, F., Macrì, P., Tancredi, A. (1986). Complexification. In: Topics on Real Analytic Spaces. Advanced Lectures in Mathematics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-84243-5_3
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DOI: https://doi.org/10.1007/978-3-322-84243-5_3
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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