Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T20:39:22.458Z Has data issue: false hasContentIssue false
  • English
  • Français

(H, C)-groups with positive line bundles

Published online by Cambridge University Press:  22 January 2016

Yukitaka Abe
Yukitaka Abe*
Affiliation:
Department of Mathematics Toyama University Gofuku, Toyama, 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 G be a connected complex Lie group. Then there exists the smallest closed complex subgroup G0 of G such that G/G0 is a Stein group (Morimoto). Moreover G0 is a connected abelian Lie group and every holomorphic function on G0 is a constant. G0 is called an (H, C)-group or a toroidal group. Every connected complex abelian Lie group is isomorphic to the direct product G0 × Cm × C*n, where G0 is an (H,C)-group.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 107 , September 1987 , pp. 1 - 11
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[1] Fujiki, A., On the blowing down of analytic spaces, Publ. RIMS Kyoto Univ., 10 (1975), 473–507.CrossRefGoogle Scholar
[2] Gherardelli, F. and Andreotti, A., Some remarks on quasi-abelian manifolds, Global analysis and its applications, Vol. II, 203–206, Intern. Atomic Energy Agency, Vienna, 1974.Google Scholar
[3] Kazama, H., Approximation theorem and application to Nakano’s vanishing theorem for weakly 1-complete manifolds, Mem. Fac. Sci. Kyushu Univ., 27 (1973), 221–240.Google Scholar
[4] Kazama, H., On pseudoconvexity of complex abelian Lie groups, J. Math. Soc. Japan, 25 (1973), 329–333.CrossRefGoogle Scholar
[5] Kazama, H., 9 cohomology of (H, C)-groups, publ. RIMS Kyoto Univ., 20 (1984), 297–317.CrossRefGoogle Scholar
[6] Kazama, H. and Umeno, T., Complex abelian Lie groups with finite-dimensional cohomology groups, J. Math. Soc. Japan, 36 (1984), 91–106.CrossRefGoogle Scholar
[7] Kopfermann, K., Maximal Untergruppen abelscher komplexer Liescher Gruppen, Schr. Math. Inst. Univ. Münster No. 29, 1964.Google Scholar
[8] Morimoto, A., Non-compact complex Lie groups without non-constant holomorphic functions, Proc. of Conf. on Complex Analysis (Minneapolis 1964), Springer-Verlag, 1965, 256–272.Google Scholar
[9] Morimoto, A., On the classification of noncompact complex abelian Lie groups, Trans. Amer. Math. Soc, 123 (1966), 200–228.CrossRefGoogle Scholar
[10] Nakano, S., On complex analytic vector bundles, J. Math. Soc. Japan, 7 (1955), 1–12.CrossRefGoogle Scholar
[11] Nakano, S., Vanishing theorems for weakly 1-complete manifolds, Number theory, algebraic geometry and commutative algebra, Kinokuniya, Tokyo, 1973.Google Scholar
[12] Pothering, G., Meromorphic function fields of non-compact Cn/T Thesis, Univ. of Notre Dame, 1977.Google Scholar
[13] Vogt, Ch., Geradenbündel auf toroiden Gruppen, Dissertation, Dusseldorf, 1981.Google Scholar
[14] Vogt, Ch., Line bundles on toroidal groups, J. reine angew. Math., 335 (1982), 197–215.Google Scholar
[15] Vogt, Ch., Two remarks concerning toroidal groups, Manuscripta Math., 41 (1983), 217–232.CrossRefGoogle Scholar