Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T23:41:42.905Z Has data issue: false hasContentIssue false
  • English
  • Français

The Continuation of sections of Torsion-Free Coherent Analytic Sheaves

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to extend the continuation theorem of holomorphic functions, especially the generalized Hartogs-Osgood’s theorem given in the previous papers [6] and [8], to the case of sections of torsion-free coherent analytic sheaves over a reduced complex space. In the following, we restrict ourselves only to reduced complex spaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 279 - 294
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Abhyankar, S., Local analytic geometry, Acad. Press, New York and London, 1964.Google Scholar
[2] Andreotti, A., Théorèmes de dépendance algébrique sur les espaces complexes pseudoconcaves, Bull. Soc. math. France, 91 (1963), 1–38.Google Scholar
[3] Andreotti, A. and Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. math. France, 90 (1962), 193–259.Google Scholar
[4] Bourbaki, N., Fasc. XXVIII. Algèbre commutativ, Paris, 1961.Google Scholar
[5] Cartan, H., Séminaire, E.N.S., 13°, 1960/1961.Google Scholar
[6] Fujimoto, H., On the continuation of analytic sets, J. Math. Soc. Japan, 18 (1966), 51–85.CrossRefGoogle Scholar
[7] Fujimoto, H., The theorem of identity for coherent analytic Modules, Nagoya Math. J., 29 (1967), 103–120.Google Scholar
[8] Fujimoto, H. and Kasahara, K., On the continuability of holomorphic functions on complex manifolds, J. Math. Soc. Japan, 16 (1964), 183–213.Google Scholar
[9] Grothendieck, A., Eléments de Géometrie Algébrique, Publ. Math. I.H.E.S., No. 4, Paris, 1960.Google Scholar
[10] Kasahara, K., On Hartogs-Osgood’s theorem for Stein spaces, J. Math. Soc. Japan, 17 (1965), 297–312.Google Scholar
[11] Scheja, G., Fortsetzungssätze der komplexe-analytischen Cohomologie und ihre algebraische Charakterisierung, Math. Ann., 157 (1964), 75–94.Google Scholar
[12] Thimm, W., Untersuchungen über das Spurproblem von holomorphen Funktionen auf analytischen Mengen, Math. Ann., 139 (1959), 95–114.Google Scholar
[13] Thimm, W., Lückengarben von koharenten analytischen Modulgarben, Math. Ann., 148 (1962), 372–394.Google Scholar