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- Title
On the -equation¶over pseudoconvex Kähler manifolds.
- Authors
Kazama, Hideaki; Takayama, Shigeharu
- Abstract
The Picard variety Pic0(? n ) of a complex n-dimensional torus? n is the group of all holomorphic equivalence classes of topologically trivial holomorphic (principal) line bundles on ? n . The total space of a topologically trivial holomorphic (principal) line bundle on a compact Kähler manifold is weakly pseudoconvex. Thus we can regard Pic0(? 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 Pic0(? n ). We get a criterion for this problem using a dynamical system of translations on Pic0(? n ). We also discuss the problem whether the -Lemma holds on strongly pseudoconvex Kähler manifolds or not. Using the result of ColColţoiu, we find a 1-convex complete Kähler manifold on which the -Lemma does not hold.
- Publication
Manuscripta Mathematica, 2000, Vol 102, Issue 1, p25
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/PL00005850