Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T10:57:01.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Holomorphic automorphisms and cancellation theorems

Published online by Cambridge University Press:  22 January 2016

Toshio Urata
Toshio Urata*
Affiliation:
Department of Mathematics, Aichi University of Education, Kariya-shi, 448 Japan
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.

Let X be a complex analytic space of positive dimension and A a complex analytic subvariety of X. We call A a direct factor of X if there exist a complex analytic space B and a biholomorphic mapping f: A × B → X such that, for some b ∊ B, f(a, b) = a on A, and a complex analytic space X to be primary if X has no direct factor, not equal to X itself, of positive dimension.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 81 , March 1981, pp. 91 - 103
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[ 1 ] Brun, J., On the cancellation problem for compact complex-analytic manifolds, Proceedings in Symposia of Pure Mathematics, 30 (1977), 247–249.Google Scholar
[ 2 ] Holmann, H., Local properties of holomorphic mappings, Proc. Conf. on Complex Analysis, Minneapolis (1964), 94–109.Google Scholar
[ 3 ] Kaneyuki, S., On the automorphism group of homogeneous bounded domains, J. Fac. Sci. Univ. Tokyo, Sect. I, 14 (1967), 89–130.Google Scholar
[ 4 ] Kobayashi, S., Hyperbolic manifolds and holomorphic mappings, Marcel Dekker. 1970.Google Scholar
[ 5 ] Kobayashi, S., Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc, 83 (1976), 357–416.CrossRefGoogle Scholar
[ 6 ] Kobayashi, S., Geometry of bounded domains, Trans. Amer. Math. Soc, 92 (1959), 267–290.CrossRefGoogle Scholar
[ 7 ] Kobayashi, S. and Nomizu, K., Foundations of differential geometry, Vol. II, Interscience Publishers, 1969.Google Scholar
[ 8 ] Peters, K., Starrheitssätze für Produkte normierte Vektorräume endlicher Dimension und für Produkte hyperbolischer komplexer Raume, Math. Ann., 208 (1974), 343–354.CrossRefGoogle Scholar
[ 9 ] Royden, H. L., Holomorphic fiber bundles with hyperbolic fiber, Proc. Amer. Math. Soc, 43 (1974), 311–312.Google Scholar
[10] Ueno, K., Classification theory of algebraic varieties and compact complex spaces, Springer Lecture Notes in Math., 439 (1975).Google Scholar
[11] Lichnerowicz, A., Variétés complexes et tenseur de Bergman, Ann. Inst. Fourier (Grenoble), 15 (1965), 345–407.Google Scholar
[12] Narasimhan, R., Introduction to the theory of analytic spaces, Springer Lecture Notes in Math., 25 (1966).Google Scholar