{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:329"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:329","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Kaehler Differential Algebras for 0-Dimensional Schemes and Applications","abstract":"The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0<m<n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1<m<6.","abstract_html":"The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0&lt;m&lt;n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1&lt;m&lt;6.","abstract_has_math":false,"creators":["Tran, Nguyen Khanh Linh"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kreuzer, Martin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-10-23","date_published":"2015-10-23","updated_at":"2026-07-24T03:45:00Z","subjects":[],"languages":[],"rights":["Standardbedingung laut Einverständniserklärung"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/329","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kreuzer, Martin"]},{"key":"dc:creator","label":"Author","values":["Tran, Nguyen Khanh Linh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"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 Passau"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Standardbedingung laut Einverständniserklärung"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0<m<n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1<m<6."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Kaehler Differential Algebras for 0-Dimensional Schemes and Applications"]}]}],"canonical_facts":{"dc:contributor":["Kreuzer, Martin"],"dc:creator":["Tran, Nguyen Khanh Linh"],"dc:description.abstract":["The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0<m<n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1<m<6."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Standardbedingung laut Einverständniserklärung"],"dc:title":["Kaehler Differential Algebras for 0-Dimensional Schemes and Applications"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:00Z"}