Geodesic
On the triviality of families of compact complex spaces
Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 335-344 
P. L. Polyakov. On the triviality of families of compact complex spaces. Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 335-344. http://geodesic.mathdoc.fr/item/SM_1969_8_3_a1/
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     author = {P. L. Polyakov},
     title = {On~the triviality of families of compact complex spaces},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper proves the following theorem (a generalization of the corresponding Grauert–Fischer theorem): if there is a holomorphic deformation $X_s$ of a compact complex space (in the sense of Serre) $X$, where the parameter $s$ of the deformation runs through the complex space $S$, and if all the $X_s$ are isomorphic to $X$, then the deformation is trivial. Bibliography: 7 titles.

[1] A. Douady, “Le probleme des modules pour les sous-espaces analytiques compactes d'un espace analytique donné”, Ann. Inst. Fourier, 16:1 (1966), 1–95 | MR | Zbl

[2] H. Grauert, W. Fischer, “Lokal-triviale Familien kompakter komplexer Mannigfaltigkeiten”, Nachr. Akad. Wiss. Göttingen, 1905, no. 6, 89–94 | MR

[3] H. Kerner, “Familien kompakter und holomorph-vollständiger komplexer Räume”, Math. Z., 92:3 (1966), 225–233 | DOI | MR | Zbl

[4] H. Grauert, H. Kerner, “Deformationen von Singularitäten komplexer Räume”, Math. Ann., 153:3 (1964), 236–260 | DOI | MR | Zbl

[5] X. Khironaka, “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki nul”, Matematika, 9:6 (1966), 2–70

[6] R. Remmert, “Holomorphe und meromorphe Abbildungen kompexer Räume”, Math. Ann., 133:4 (1957), 328–370 | DOI | MR | Zbl

[7] G. Grauert, “Odna teorema iz teorii analiticheskikh puchkov”, Kompleksnye prostranstva, Mir, M., 1965 | MR