Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-02-05T08:50:00.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Families of smooth hypersurfaces on certain compact homogeneous complex manifolds

Published online by Cambridge University Press:  24 October 2008

Ciprian Borcea
Ciprian Borcea
Affiliation:
Department of Mathematics, National Institute for Scientific and Technical Creation, Bucharest
Get access Rights & Permissions [Opens in a new window]

Extract

Let X be a compact connected homogeneous complex manifold, which is Kāhlerian and has the second Betti number equal to one: b2(X) = 1; dimcX ≥ 3.

It is known that these conditions imply the following: X is a projective-rational homogeneous manifold (see (3)); X has an ‘algebraic cell-decomposition’: the 2s-dimensional closed cells are s-dimensional irreducible algebraic sets in X and they form a basis for the 2s-homology group of X, s = 1, 2, …, dimcX (see (1)); there are no holomorphic maps of X on lower dimensional (normal) analytic spaces except constants (see (9)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 315 - 321
Copyright
Copyright © Cambridge Philosophical Society 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borel, A.Kählerian coset spaces of semi-simple Lie groups. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1147–1151.CrossRefGoogle Scholar
(2)Borel, A. and Hirzebruch, F.Characteristic classes and homogeneous spaces. I. Amer. J. Math. 80 (1958), 458–538.CrossRefGoogle Scholar
(3)Borel, A. and Remmert, R.Über kompakte homogene Kählersche Mannigfaltigkeiten. Math. Ann. 145 (1962), 429–439.CrossRefGoogle Scholar
(4)Borel, A. and Weil, A. (report by J. P. Serre). Représentations linéaires et espaces homogenes Kählériens des groupes deLie compacts. Séminaire Bourbaki (05, 1954), exp. 100.Google Scholar
(5)Bott, R.Homogeneous vector bundles. Awn. of Math. 66 (1957), 203–248.Google Scholar
(6)Humphreys, J. E.Introduction to Lie algebras and representation theory (Springer-Verlag, New York, Heidelberg, Berlin, 1972).Google Scholar
(7)Kodaira, K. and Spencer, D. C.On deformation of complex analytic structures. I–II. Ann. of Math. 67 (1958), 328–466.CrossRefGoogle Scholar
(8)Kodaira, K. and Spencer, D. C.A theorem of completeness for complex analytic fibre spaces. Acta Mathematica. 100 (1958), 281–294.CrossRefGoogle Scholar
(9)Remmert, R. and Van De Ven, T.Über holomorphe Abbildungen projektiv-algebraischer Mannigfaltigkeiten auf komplexe Raume. Math. Ann. 142 (1961), 453–486.Google Scholar