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Article: Fibrations of compact Kahler manifolds in terms of cohomological properties of their fundamental groups

TitleFibrations of compact Kahler manifolds in terms of cohomological properties of their fundamental groups
Authors
Issue Date2000
PublisherAssociation des Annales de l'Institut Fourier. The Journal's web site is located at http://www-fourier.ujf-grenoble.fr/
Citation
Annales de l'institut Fourier, 2000, v. 50 n. 2, p. 633-675 How to Cite?
AbstractWe prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group Γ of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H1(Γ, Φ) ≠ 0 for some unitary representation Φ. By our earlier work there exists a d-closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ', possibly non-isomorphic to Φ. Taking norms we obtains a positive semi-definite d-closed (1,1)-form ν on X, which underlies a semi-Khäler structure. We study meromorphic foliations related to this semi-Khäler structure and another semi-Khäler structure related to the Ricci form to prove fibration theorems on some modification of an unramified finite cover of X. The base manifold is shown to be either a compact complex torus or a variety of logarithmic general type with respect to the multiplicity locus of the holomorphic fibration.
Persistent Identifierhttp://hdl.handle.net/10722/75396
ISSN
2015 Impact Factor: 0.494
2015 SCImago Journal Rankings: 1.492

 

DC FieldValueLanguage
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2010-09-06T07:10:43Z-
dc.date.available2010-09-06T07:10:43Z-
dc.date.issued2000en_HK
dc.identifier.citationAnnales de l'institut Fourier, 2000, v. 50 n. 2, p. 633-675en_HK
dc.identifier.issn0373-0956-
dc.identifier.urihttp://hdl.handle.net/10722/75396-
dc.description.abstractWe prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group Γ of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H1(Γ, Φ) ≠ 0 for some unitary representation Φ. By our earlier work there exists a d-closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ', possibly non-isomorphic to Φ. Taking norms we obtains a positive semi-definite d-closed (1,1)-form ν on X, which underlies a semi-Khäler structure. We study meromorphic foliations related to this semi-Khäler structure and another semi-Khäler structure related to the Ricci form to prove fibration theorems on some modification of an unramified finite cover of X. The base manifold is shown to be either a compact complex torus or a variety of logarithmic general type with respect to the multiplicity locus of the holomorphic fibration.-
dc.languageengen_HK
dc.publisherAssociation des Annales de l'Institut Fourier. The Journal's web site is located at http://www-fourier.ujf-grenoble.fr/-
dc.relation.ispartofAnnales de l'institut Fourieren_HK
dc.titleFibrations of compact Kahler manifolds in terms of cohomological properties of their fundamental groupsen_HK
dc.typeArticleen_HK
dc.identifier.emailMok, N: nmok@hkucc.hku.hken_HK
dc.identifier.authorityMok, N=rp00763en_HK
dc.identifier.doi10.5802/aif.1767-
dc.identifier.hkuros53194en_HK
dc.identifier.volume50-
dc.identifier.issue2-
dc.identifier.spage633-
dc.identifier.epage675-
dc.publisher.placeFrance-

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