{"id":{"repo_id":"oldenburg","oai_identifier":"oai:oops.uni-oldenburg.de:125"},"canonical_url":"https://search.dev.ndltd.org/etd/oldenburg/oai:oops.uni-oldenburg.de:125","repository":{"repo_id":"oldenburg","name":"Carl von Ossietzky Universität Oldenburg","base_url":"http://oops.uni-oldenburg.de/cgi/oai2"},"display":{"title":"Generalized Koszul complexes","abstract":"We introduce Koszul type complexes associated to a linear map from any module to a free module, and vice versa to a linear map from a free module to an arbitrary module, generalizing both the classical Koszul complex and the family of Eagon-Northcott complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complex this homology is found to be grade sensitive. In a special setup we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.","abstract_html":"We introduce Koszul type complexes associated to a linear map from any module to a free module, and vice versa to a linear map from a free module to an arbitrary module, generalizing both the classical Koszul complex and the family of Eagon-Northcott complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complex this homology is found to be grade sensitive. In a special setup we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.","abstract_has_math":false,"creators":["Ichim, Bogdan"],"institution":"Universität Oldenburg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-12-17","date_published":"2004-12-17","updated_at":"2026-07-27T20:27:13Z","subjects":["[Keine Schlagwörter von Autor/in vergeben.]"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://oops.uni-oldenburg.de/125","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ichim, Bogdan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["BIS der Universität Oldenburg"]},{"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 Oldenburg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["[Keine Schlagwörter von Autor/in vergeben.]"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce Koszul type complexes associated to a linear map from any module to a free module, and vice versa to a linear map from a free module to an arbitrary module, generalizing both the classical Koszul complex and the family of Eagon-Northcott complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complex this homology is found to be grade sensitive. In a special setup we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.","Wir betrachten Koszul-Komplexe linearer Abbildungen in und von freien Moduln. Dabei handelt es sich um eine Verallgemeinerung sowohl des klassischen Koszul-Komplexes als auch der Familie von Eagon-Northcott-Komplexen. Ausgehend von einem kurzen Komplex endlicher freier Moduln werden diese Komplexe zu sogenannten Koszul-Bikomplexen zusammengefügt. Damit läßt sich die Homologie von Koszul-Komplexen in der projektiven Dimension 1 untersuchen. Wie im klassischen Fall erweist sich diese Homologie als grad-sensitiv. Überdies erhalten wir - in einem speziellen Zusammenhang - notwendige Bedingungen dafür, wann sich eine Abbildung freier Moduln zu einem kurzen Komplex freier Moduln verlängern läßt."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Generalized Koszul complexes"]}]}],"canonical_facts":{"dc:creator":["Ichim, Bogdan"],"dc:description.abstract":["We introduce Koszul type complexes associated to a linear map from any module to a free module, and vice versa to a linear map from a free module to an arbitrary module, generalizing both the classical Koszul complex and the family of Eagon-Northcott complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complex this homology is found to be grade sensitive. In a special setup we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.","Wir betrachten Koszul-Komplexe linearer Abbildungen in und von freien Moduln. Dabei handelt es sich um eine Verallgemeinerung sowohl des klassischen Koszul-Komplexes als auch der Familie von Eagon-Northcott-Komplexen. Ausgehend von einem kurzen Komplex endlicher freier Moduln werden diese Komplexe zu sogenannten Koszul-Bikomplexen zusammengefügt. Damit läßt sich die Homologie von Koszul-Komplexen in der projektiven Dimension 1 untersuchen. Wie im klassischen Fall erweist sich diese Homologie als grad-sensitiv. Überdies erhalten wir - in einem speziellen Zusammenhang - notwendige Bedingungen dafür, wann sich eine Abbildung freier Moduln zu einem kurzen Komplex freier Moduln verlängern läßt."],"dc:format.medium":["application/pdf"],"dc:publisher":["BIS der Universität Oldenburg"],"dc:subject":["[Keine Schlagwörter von Autor/in vergeben.]"],"dc:title":["Generalized Koszul complexes"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Oldenburg"]},"updated_at":"2026-07-27T20:27:13Z"}