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The Theorem of Identity for Coherent Analytic Modules

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya Institute of Technology
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The theorem of identity for analytic subsets of a reduced complex space is stated as follows;

Let V and V′ be two analytic subsets of a reduced complex space. If V is irreducible and there exists a point x ∊ V such that the germ Vx of V at x is included in V′x, then V is included in V′.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 103 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Abhyankar, S., Concepts of order and rank on a complex space and a condition for normality, Math. Ann., 141 (1960), pp. 171–192.CrossRefGoogle Scholar
[2] Bourbaki, N., Fase. XXVIII. Algebre commutativ. Chap. 4; Idéaux premiers associéset décomposition primaire, Paris, 1–961.Google Scholar
[3] Cartan, H., Séminaire, E. N. S., 1951/1952.Google Scholar
[4] Cartan, H., Séminaire, E. N. S., 13, 1960/1961.Google Scholar
[5] Fujimoto, H., On the continuation of analytic sets, J. of Math. Soc. Japan, 18 (1966), pp. 51–85.Google Scholar
[6] Forster, O., Primärzerlegung in Steinschen Algebren, Math, Ann., 154 (1964), pp. 307–329.Google Scholar
[7] Grauert, H., Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Publ. Math. I.H.E.S., No. 5, Paris 1960.Google Scholar
[8] Grothendieck, A., Eléments de Géométrie Algébrique, Publ. Math. I.H.E,S., No. 4, Paris 1960.Google Scholar
[9] Kuhlmann, N., Über die nor mal en Punkte eines komplexen Raumes, Math. Ann., 146 (1962), pp. 397–412.CrossRefGoogle Scholar
[10] Northcott, D. G., Ideal theory, Cambridge Univ. Press, Cambridge, 1953.CrossRefGoogle Scholar
[11] Remmert, R. and Stein, K., Über die wesentlichen singularitàten analytischer Mengen, Math. Ann., 126 (1953), pp. 263–306.Google Scholar
[12] Rothstein, W., Zur Théorie der analytischen Mannigfaltigkeiten im Raum vonn komplexen Veränderlichen, Math. Ann., 129 (1955), pp. 96–138.CrossRefGoogle Scholar
[13] Scheja, G., Fortsetzungssätze der komplexe analytischen Cohomologie und ihre algebraische Chaiakterisierung, Math. Ann., 157 (1964), pp. 75–94.CrossRefGoogle Scholar
[14] Thimm, W., Luckengarben von kohärenten analytischen Modulgarben, Math. Ann., 148 (1962), pp. 372–394.Google Scholar