-problem on weakly 1-complete Kähler manifolds

Kazama, Hideaki; Takayama, Shigeharu

doi:10.1017/s0027763000007005

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Proof Of the Results1

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2000

2024

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Cited by 7 publications

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References 10 publications

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“…Now, it was shown in Theorem 1, p. 686 of [8] (see also [9], [15] and [16]), that for E ∈ R * the cohomology group H 1 (E, O E ) is not Hausdorff.…”

Section: Proof Of the Resultsmentioning

confidence: 99%

A remark on non-Hausdorff cohomology groups of analytic complements

Colţoiu¹,

Diederich²

2002

Mathematische Annalen

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“…Now, it was shown in Theorem 1, p. 686 of [8] (see also [9], [15] and [16]), that for E ∈ R * the cohomology group H 1 (E, O E ) is not Hausdorff.…”

Section: Proof Of the Resultsmentioning

confidence: 99%

A remark on non-Hausdorff cohomology groups of analytic complements

Colţoiu¹,

Diederich²

2002

Mathematische Annalen

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“…In the previous paper [7] it is shown that on some class of weakly pseudoconvex Kähler manifolds (the so-called quasi-tori) the ∂∂-Lemma holds, furthermore there exist weakly pseudoconvex Kähler manifolds on which the ∂∂-Lemma does not hold. The second named author [15] showed that a weak form of ∂∂-Lemma holds for every quasi-torus.…”

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confidence: 99%

On the -equation¶over pseudoconvex Kähler manifolds

Kazama¹,

Takayama²

2000

manuscripta math.

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The Picard variety Pic 0 (T n ) of a complex n-dimensional torus T n is the group of all holomorphic equivalence classes of topologically trivial holomorphic (principal) line bundles on T n . The total space of a topologically trivial holomorphic (principal) line bundle on a compact Kähler manifold is weakly pseudoconvex. Thus we can regard Pic 0 (T n ) as a family of weakly pseudoconvex Kähler manifolds. We consider a problem whether the Kodaira's ∂∂-Lemma holds on a total space of holomorphic line bundle belonging to Pic 0 (T n ). We get a criterion for this problem using a dynamical system of translations on Pic 0 (T n ). We also discuss the problem whether the ∂∂-Lemma holds on strongly pseudoconvex Kähler manifolds or not. Using the result of Colţoiu, we find a 1-convex complete Kähler manifold on which the ∂∂-Lemma does not hold.

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Very ample line bundles on quasi-abelian varieties

Takayama¹

2001

Math Z

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-problem on weakly 1-complete Kähler manifolds

Cited by 7 publications

References 10 publications

A remark on non-Hausdorff cohomology groups of analytic complements

A remark on non-Hausdorff cohomology groups of analytic complements

On the -equation¶over pseudoconvex Kähler manifolds

Very ample line bundles on quasi-abelian varieties

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