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Campana, F.

Reduction algébrique d’un morphisme faiblement Kählerien propre et applications. (French) Zbl 0461.32010

Math. Ann. 256, 157-189 (1981).
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Cited in 2 Reviews
Cited in 9 Documents

MSC:

32J99 Compact analytic spaces
32H99 Holomorphic mappings and correspondences
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32A20 Meromorphic functions of several complex variables
32D15 Continuation of analytic objects in several complex variables

Keywords:

algebraic dimension; compact complex analytic cycles; space of cycles; analytic Kählerian space; algebraic reduction for Kählerian morphism
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\textit{F. Campana}, Math. Ann. 256, 157--189 (1981; Zbl 0461.32010)
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References:

[1] [B1] Barlet, D.: Familles analytiques de cycles. In: Fonctions de plusieurs variables complexes II. Séminaire Norguet. Lecture Notes in Mathematics, Vol. 482, pp. 1-158. Berlin, Heidelberg, New York: Springer 1975
[2] [B2] Barlet, D.: Convexité de l’espace des cycles. Bull. Soc. Math. France106, 373-397 (1978) · Zbl 0395.32009
[3] [B3] Barlet, D.: Majoration de volume et forme géométrique du théorème d’aplatissement, C. R. Acad. Sci.288, (1979) et séminaire Lelong (1978-1979)
[4] [C1] Campana, F.: Images directes de cycles par un morphisme. In: Fonctions de plusieurs variables complexes. IV. Séminaire Norguet. Lecture Notes in Mathematics, Vol. 807, pp. 25-65. Berlin Heidelberg, New York: Springer 1980
[5] [C2] Campana, F.: Algébricité et compacité dans l’espace des cycles. C. R. Acad. Sci.289 (1979) et Math. Ann.251, 7-18 (1980)
[6] [C3] Campana, F.: Diviseurs non-polaires (submitted for publication)
[7] [C4] Campana, F.: Application de l’espace des cycles. Prepublication Université Nancy I (Mai 1980)
[8] [C5] Campana, F.: Coréduction d’un espace analytique faiblement Kählérien compact. Invent. Math.63, 187-223 (1981) · Zbl 0447.32009
[9] [F] Fischer, G.: Complex analytic geometry. In: Lecture Notes in Mathematics, Vol. 538, Berlin, Heidelberg, New York: Springer 1976 · Zbl 0343.32002
[10] [F-F] Fischer, G., Forster, O.: Ein Endlichkeitssatz für Hyperflächen auf kompakten komplexen Räumen. J. Reine Angew Math.306, 88-93 (1979) · Zbl 0395.32004
[11] [F1] Fujiki, A.: Closedness of the Douady space of a compact Kähler space. Publ. Res. Inst. Math. Sci.14, 1-52 (1978) · Zbl 0409.32016
[12] [F2] Fujiki, A.: On the Douady space of a compact space in the categoryC (Submitted for publication)
[13] [G] Grothendieck, A.: Techniques de construction en géométrie analytique. Séminaire Cartan (1960/61)
[14] [U] Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. In: Lecture Notes in Mathematics, Vol. 493. Berlin, Heidelberg, New York: Springer 1975 · Zbl 0299.14007
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