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Toroidal groups: line bundles, cohomology and quasi-Abelian varieties

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Bibliographic Details
Main Authors:	Abe, Yukitaka (Author), Kopfermann, Klaus (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2001
Series:	Lecture notes in mathematics 1759
Subjects:	Toroid <Gruppentheorie> Toroid > Gruppentheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 133 S.
ISBN:	3540419896

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MARC


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adam_text	Contents Introduction 1 1. The Concept of Toroidal Groups 3 1.1 Irrationality and toroidal coordinates 3 Toroidal groups 3 Complex homomorphisms 7 Toroidal coordinates and C ~* fibre bundles 9 Maximal Stein subgroups of toroidal groups 14 1.2 Toroidal subgroups and pseudoconvexity 16 The maximal toroidal subgroup of a complex Lie group 16 Pseudoconvexity 19 The maximal complex subtorus of a complex Lie group 22 2. Line Bundles and Cohomology 25 2.1 Line bundles on toroidal groups 25 Automorphic factors 25 The characteristic decomposition of an exponential system 28 Automorphic summands 32 Theta bundles and topologically trivial line bundles 37 2.2 Cohomology of toroidal groups 44 Toroidal theta and wild groups 44 Dolbeault cohomology of toroidal theta groups 47 Dolbeault cohomology of complex Lie groups 54 3. Quasi Abelian Varieties 57 3.1 Ample Riemann forms 57 The Hermitian decomposition of an automorphic factor 57 Period relations 61 Ample Riemann forms 64 Maximal Stein subgroups of quasi Abelian varieties 68 3.2 Characterization of quasi Abelian varieties 73 Cohomology and the average of differential forms 73 VIII Contents Chern forms of fibre metrics 80 Holomorphic mappings to projective spaces 85 Meromorphic functions on toroidal groups 88 4. Reduction and Extension 93 4.1 Automorphic forms 93 Reduction to the positive definite case 93 Further properties of meromorphic functions 101 Existence of automorphic forms and Lefschetz type theorems.... 103 4.2 Extendable line bundles 106 The case of C* ~Â« fibre bundles 106 The case of kind Â£ 113 Explicit representation of automorphic forms 120 References 125 Index 131
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indexdate	2024-07-09T18:50:23Z
institution	BVB
isbn	3540419896
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009358952
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open_access_boolean
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physical	VIII, 133 S.
publishDate	2001
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series	Lecture notes in mathematics
series2	Lecture notes in mathematics
spelling	Abe, Yukitaka Verfasser aut Toroidal groups line bundles, cohomology and quasi-Abelian varieties Yukitaka Abe ; Klaus Kopfermann Berlin [u.a.] Springer 2001 VIII, 133 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1759 Toroid <Gruppentheorie> Toroid Gruppentheorie (DE-588)4642415-5 gnd rswk-swf Toroid Gruppentheorie (DE-588)4642415-5 s DE-604 Kopfermann, Klaus Verfasser aut Lecture notes in mathematics 1759 (DE-604)BV000676446 1759 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Abe, Yukitaka Kopfermann, Klaus Toroidal groups line bundles, cohomology and quasi-Abelian varieties Lecture notes in mathematics Toroid <Gruppentheorie> Toroid Gruppentheorie (DE-588)4642415-5 gnd
subject_GND	(DE-588)4642415-5
title	Toroidal groups line bundles, cohomology and quasi-Abelian varieties
title_auth	Toroidal groups line bundles, cohomology and quasi-Abelian varieties
title_exact_search	Toroidal groups line bundles, cohomology and quasi-Abelian varieties
title_full	Toroidal groups line bundles, cohomology and quasi-Abelian varieties Yukitaka Abe ; Klaus Kopfermann
title_fullStr	Toroidal groups line bundles, cohomology and quasi-Abelian varieties Yukitaka Abe ; Klaus Kopfermann
title_full_unstemmed	Toroidal groups line bundles, cohomology and quasi-Abelian varieties Yukitaka Abe ; Klaus Kopfermann
title_short	Toroidal groups
title_sort	toroidal groups line bundles cohomology and quasi abelian varieties
title_sub	line bundles, cohomology and quasi-Abelian varieties
topic	Toroid <Gruppentheorie> Toroid Gruppentheorie (DE-588)4642415-5 gnd
topic_facet	Toroid <Gruppentheorie> Toroid Gruppentheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009358952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT abeyukitaka toroidalgroupslinebundlescohomologyandquasiabelianvarieties AT kopfermannklaus toroidalgroupslinebundlescohomologyandquasiabelianvarieties

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