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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
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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

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References

REFERENCES

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