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We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces ...
Abstract: Pittie [Pit88] proved that the Dolbeault cohomology of all left-invariant complex structures on compact Lie groups can be computed by looking at the Dolbeault cohomology induced ...
Abstract: Pittie [Pit88] proved that the Dolbeault cohomology of all left-invariant complex structures on compact Lie groups can be computed by looking at the Dolbeault cohomology induced ...
sequence is computed in cases connected with the Dirac operator in two Clifford variables. Mathematics Subject Classification (2000). Primary 58J70; Secondary 30G35. Keywords. Generalized Dolbeault complex ...
For a simply connected (non-nilpotent) solvable Lie group G with a lattice Γ the de Rham and Dolbeault cohomologies of the solvmanifold G/Γ are not in general isomorphic to the cohomologies ...
on complex manifolds, which is related to the complex structures of complex manifolds. In general cases, the computation of Dol- beault cohomology is much more difficult than that of de Rham one. One reason ...
Pittie (Proc Indian Acad Sci Math Sci 98:117-152, 1988) proved that the Dolbeault cohomology of all left-invariant complex structures on compact Lie groups can be computed by looking at the Dolbeault ...
. The main tool is the Leray spectral sequence that connects the result obtained Chevalley and Eilenberg to a result by Bott on the Dolbeault cohomology of a homogeneous manifold. Inspired by the work ...
of a one dimensional torus in K. We compute the Dolbeault cohomology of W. We compute the Picard group of any generalized Hopf manifold and show that every ...
image, and apply the Peter-Weyl theorem to show how q determines the value 0 or $\infty$ . For the case when P is maximal, we apply our result to compute the Dolbeault cohomology of certain examples ...
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