Formal modifications. Existence theorems for modifications of complex manifolds
Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 847-881.

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For the existence of a nonsingular contraction (dilatation) of an analytic set on an $n$-dimensional complex manifold it is proved to be necessary and sufficient that there exist a formal nonsingular contraction (dilatation) of the analytic set.
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V. A. Krasnov. Formal modifications. Existence theorems for modifications of complex manifolds. Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 847-881. http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a5/

[1] Kartan A., “Faktorprostranstva analiticheskikh prostranstv”, Kompleksnye prostranstva, Mir, M., 1965, 29–44 | MR

[2] Artin M., “Algebraization of formal moduli. II: Existence of modifications”, Ann. Math., 91:1 (1970), 88–135 | DOI | MR

[3] Krasnov V. A., “Deformatsii kompleksno-analiticheskikh modifikatsii”, Izv. AN SSSR. Ser. matem., 37 (1973), 516–532 | MR | Zbl

[4] Grothendieck A., “Éléments de géométrie algébrique. I: Le langage des schémas”, Inst. Hautes Études Sci. Publ. Math., 1960, no. 4, 5–228 | DOI | MR

[5] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968

[6] Grothendieck A., “Éléments de géométrie algébrique. III: Étude cohomologique des faisceaux coherents, Publications”, Inst. Hautes Études Sci. Publ. Math., 1961, no. 11, 349–511

[7] Grauert H., Remmert R., “Bilder und Urbilder analytischer Graben”, Ann. Math., ser. 2, 68:2 (1958), 393–443 | DOI | MR | Zbl

[8] Malgrange B., “Sur les fonctions différentiables et ensembles analytiques”, Bull. Soc. Math. France, 91 (1963), 113–127 | MR | Zbl

[9] Khironaka Kh., “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki nul”, Matematika, 9:6 (1965), 2–70; 10:1 (1966), 3–89 ; 10:2 (1966), 3–58 | MR | MR

[10] Hironaka H., “A Fundamental Lemma on Point Modifications”, Proceedings of the Conference on Complex Analysis (Minneapolis, 1964), Springer-Verlag, Berlin, Heidelberg, New York, 1965, 194–215 | MR

[11] Hironaka H., Rossi H., “On the equivalence of imbedings of exceptional complex spaces”, Math. Ann., 156:4 (1964), 313–333 | DOI | MR | Zbl

[12] Remmert R., “Holomorphe und meromorphe Abbildungen komplexer Räume”, Math. Ann., 133:3 (1957), 328–370 | DOI | MR | Zbl