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This article is cited in 4 scientific papers (total in 4 papers)
Comology of compact complex homogeneous spaces
D. N. Akhiezer
Abstract:
In this paper we study compact complex homogeneous spaces having a complex torus for the fiber of the canonical fibration (Tits fibration). We prove that the cohomology of such a space $X$ with coefficients in the sheaf of germs of holomorphic sections of the homogeneous linear fibration $\mathbf E$ is nonzero only if $\mathbf E$ is the inverse image of some fibration $\widetilde{\mathbf E}$ over a base $D$ of the canonical fibration. In this case the representation in $H^*(X,\mathbf E)$ can be computed using a spectral sequence if we know the representation in $H^*(D,\widetilde{\mathbf E})$. The resulting theorem generalizes Griffiths' result for $C$-spaces.
Bibliography: 8 titles.
Received: 03.03.1970
Citation:
D. N. Akhiezer, “Comology of compact complex homogeneous spaces”, Math. USSR-Sb., 13:2 (1971), 285–296
Linking options:
https://www.mathnet.ru/eng/sm3073https://doi.org/10.1070/SM1971v013n02ABEH001892 https://www.mathnet.ru/eng/sm/v126/i2/p290
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