{"id":{"repo_id":"bayreuth","oai_identifier":"oai:epub.uni-bayreuth.de:157"},"canonical_url":"https://search.dev.ndltd.org/etd/bayreuth/oai:epub.uni-bayreuth.de:157","repository":{"repo_id":"bayreuth","name":"Universität Bayreuth","base_url":"https://epub.uni-bayreuth.de/cgi/oai2"},"display":{"title":"THE INDEX THEOREM FOR QUASI-TORI","abstract":"The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.","abstract_html":"The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.","abstract_has_math":false,"creators":["Chan, Tsz On Mario"],"institution":"Universität Bayreuth","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Catanese, Fabrizio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-11-27","date_published":"2012-11-27","updated_at":"2026-07-27T18:49:06Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://epub.uni-bayreuth.de/id/eprint/157/","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Catanese, Fabrizio"]},{"key":"dc:creator","label":"Author","values":["Chan, Tsz On Mario"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Bayreuth"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Bayreuth"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.","Der Index-Satz für holomorphe Geradenbündel über komplexen Tori besagt, dass einige Kohomologiegruppen eines solchen Geradenbündels verschwinden, und zwar in Abhängigkeit von der Anzahl der negativen und positiven Eigenwerte der zugehörigen hermiteschen Form. In dieser Arbeit wird dieses Theorem auf Quasi-Tori, d.h. zusammenhängende komplexe abelschen Lie-Gruppen, die nicht unbedingt kompakt sind, verallgemeinert. In Anbetracht der Remmert–Morimoto Zerlegung von Quasi-Tori und der Künneth Formel genügt es Cousin-Quasi-Tori zu betrachten, d.h. Quasi-Tori ohne nicht-konstante holomorphe Funktionen. Es werden L2-Methoden zusammen mit dem Kazama–Dolbeault Isomorphismus und Bochner–Kodaira-Formeln verwendet, um den Index- Satz auf den Fall von holomorphen Geradenbündeln auf Cousin-Quasi- Tori zu verallgemeinern. Dabei sind linearisierbare und nicht-linearisierbare Geradenbündel zugelassen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["THE INDEX THEOREM FOR QUASI-TORI"]}]}],"canonical_facts":{"dc:contributor":["Catanese, Fabrizio"],"dc:creator":["Chan, Tsz On Mario"],"dc:description.abstract":["The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.","Der Index-Satz für holomorphe Geradenbündel über komplexen Tori besagt, dass einige Kohomologiegruppen eines solchen Geradenbündels verschwinden, und zwar in Abhängigkeit von der Anzahl der negativen und positiven Eigenwerte der zugehörigen hermiteschen Form. In dieser Arbeit wird dieses Theorem auf Quasi-Tori, d.h. zusammenhängende komplexe abelschen Lie-Gruppen, die nicht unbedingt kompakt sind, verallgemeinert. In Anbetracht der Remmert–Morimoto Zerlegung von Quasi-Tori und der Künneth Formel genügt es Cousin-Quasi-Tori zu betrachten, d.h. Quasi-Tori ohne nicht-konstante holomorphe Funktionen. Es werden L2-Methoden zusammen mit dem Kazama–Dolbeault Isomorphismus und Bochner–Kodaira-Formeln verwendet, um den Index- Satz auf den Fall von holomorphen Geradenbündeln auf Cousin-Quasi- Tori zu verallgemeinern. Dabei sind linearisierbare und nicht-linearisierbare Geradenbündel zugelassen."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Bayreuth"],"dc:title":["THE INDEX THEOREM FOR QUASI-TORI"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Bayreuth"]},"updated_at":"2026-07-27T18:49:06Z"}