{"id":{"repo_id":"bayreuth","oai_identifier":"oai:epub.uni-bayreuth.de:209"},"canonical_url":"https://search.dev.ndltd.org/etd/bayreuth/oai:epub.uni-bayreuth.de:209","repository":{"repo_id":"bayreuth","name":"Universität Bayreuth","base_url":"https://epub.uni-bayreuth.de/cgi/oai2"},"display":{"title":"Irreducible symplectic complex spaces","abstract":"In Chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such period mappings as the composition of the Kodaira-Spencer map and a map derived from the sheaf cohomological cup product and the contraction of vector fields with differential forms. In Chapter 2 of the text, we consider a submersive morphism $f\\colon X\\to S$ of complex spaces which is compactified by a proper, flat, and Kähler morphism $\\bar f\\colon \\bar X\\to S$. Taking into account the codimension of $\\bar X\\setminus X$ in $\\bar X$, we draw conclusions about the degeneration behavior of the relative Frölicher spectral sequence of the morphism $f$ and about the local freeness of the modules $\\mathrm{R}^qf_*(\\Omega^p_f)$; our results can be viewed as relative generalizations of a theorem of Takeo Ohsawa. In our final Chapter 3, we employ the upshots of the preceding two chapters in order to deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.","abstract_html":"In Chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths&#x27;s theory, we interpret the differential of such period mappings as the composition of the Kodaira-Spencer map and a map derived from the sheaf cohomological cup product and the contraction of vector fields with differential forms. In Chapter 2 of the text, we consider a submersive morphism $f\\colon X\\to S$ of complex spaces which is compactified by a proper, flat, and Kähler morphism $\\bar f\\colon \\bar X\\to S$. Taking into account the codimension of $\\bar X\\setminus X$ in $\\bar X$, we draw conclusions about the degeneration behavior of the relative Frölicher spectral sequence of the morphism $f$ and about the local freeness of the modules <span class=\"etd-inline-math\"><span class=\"etd-inline-math-roman\">R</span><sup>q</sup>f<sub>*</sub>(\\Omega<sup>p</sup><sub>f</sub>)</span>; our results can be viewed as relative generalizations of a theorem of Takeo Ohsawa. In our final Chapter 3, we employ the upshots of the preceding two chapters in order to deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.","abstract_has_math":true,"creators":["Kirschner, Tim"],"institution":"Universität Bayreuth","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Peternell, Thomas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-10-02","date_published":"2012-10-02","updated_at":"2026-07-27T18:49:06Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://epub.uni-bayreuth.de/id/eprint/209/","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Peternell, Thomas"]},{"key":"dc:creator","label":"Author","values":["Kirschner, Tim"]}]},{"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":["In Chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such period mappings as the composition of the Kodaira-Spencer map and a map derived from the sheaf cohomological cup product and the contraction of vector fields with differential forms. In Chapter 2 of the text, we consider a submersive morphism $f\\colon X\\to S$ of complex spaces which is compactified by a proper, flat, and Kähler morphism $\\bar f\\colon \\bar X\\to S$. Taking into account the codimension of $\\bar X\\setminus X$ in $\\bar X$, we draw conclusions about the degeneration behavior of the relative Frölicher spectral sequence of the morphism $f$ and about the local freeness of the modules $\\mathrm{R}^qf_*(\\Omega^p_f)$; our results can be viewed as relative generalizations of a theorem of Takeo Ohsawa. In our final Chapter 3, we employ the upshots of the preceding two chapters in order to deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.","In Kapitel 1 definieren wir Periodenabbildungen von Hodge-de Rahm'schem Typ für gewisse submersive, jedoch nicht notwendigerweise lokal topologisch triviale, Morphismen komplexer Mannigfaltigkeiten. Wir interpretieren das Differential dieser Periodenabbildungen, in Verallgemeinerung der Griffiths'schen Theorie, als Verkettung der Kodaira-Spencer'schen Abbildung mit einer Abbildung, die aus dem garbenkohomologischen Cup-Produkt und der Kontraktion von Vektorfeldern mit Differentialformen gewonnen werden kann. Im zweiten Kapitel der Arbeit betrachten wir submersive Morphismen $f\\colon X\\to S$ komplexer Räume, die über einen eigentlichen, flachen und Kähler'schen Morphismus $\\bar f \\colon \\bar X \\to S$ kompaktifiziert sind. Aus der Kodimension der Differenzmenge $\\bar X \\setminus X$ in $\\bar X$ ziehen wir Rückschlüsse auf das Degenerationsverhalten der relativen Frölicher'schen Spektralsequenz des Morphismus $f$ und auf die lokale Freiheit der Moduln $\\mathrm{R}^qf_*(\\Omega^p_f)$; unsere Ergebnisse können als relative Verallgemeinerungen eines Satzes von Takeo Ohsawa angesehen werden. Im dritten Kapitel unserer Arbeit verwenden wir schließlich die Resultate der beiden vorherigen Kapitel, um einen lokalen Torelli'schen Satz für irreduzibel symplektische komplexe Räume herzuleiten. Als Anwendung des Torelli'schen Satzes zeigen wir, dass irreduzibel symplektische komplexe Räume, deren singulärer Ort eine Kodimension von $4$ oder größer besitzt, der sogenannten Fujiki-Relation genügen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Irreducible symplectic complex spaces"]}]}],"canonical_facts":{"dc:contributor":["Peternell, Thomas"],"dc:creator":["Kirschner, Tim"],"dc:description.abstract":["In Chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such period mappings as the composition of the Kodaira-Spencer map and a map derived from the sheaf cohomological cup product and the contraction of vector fields with differential forms. In Chapter 2 of the text, we consider a submersive morphism $f\\colon X\\to S$ of complex spaces which is compactified by a proper, flat, and Kähler morphism $\\bar f\\colon \\bar X\\to S$. Taking into account the codimension of $\\bar X\\setminus X$ in $\\bar X$, we draw conclusions about the degeneration behavior of the relative Frölicher spectral sequence of the morphism $f$ and about the local freeness of the modules $\\mathrm{R}^qf_*(\\Omega^p_f)$; our results can be viewed as relative generalizations of a theorem of Takeo Ohsawa. In our final Chapter 3, we employ the upshots of the preceding two chapters in order to deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.","In Kapitel 1 definieren wir Periodenabbildungen von Hodge-de Rahm'schem Typ für gewisse submersive, jedoch nicht notwendigerweise lokal topologisch triviale, Morphismen komplexer Mannigfaltigkeiten. Wir interpretieren das Differential dieser Periodenabbildungen, in Verallgemeinerung der Griffiths'schen Theorie, als Verkettung der Kodaira-Spencer'schen Abbildung mit einer Abbildung, die aus dem garbenkohomologischen Cup-Produkt und der Kontraktion von Vektorfeldern mit Differentialformen gewonnen werden kann. Im zweiten Kapitel der Arbeit betrachten wir submersive Morphismen $f\\colon X\\to S$ komplexer Räume, die über einen eigentlichen, flachen und Kähler'schen Morphismus $\\bar f \\colon \\bar X \\to S$ kompaktifiziert sind. Aus der Kodimension der Differenzmenge $\\bar X \\setminus X$ in $\\bar X$ ziehen wir Rückschlüsse auf das Degenerationsverhalten der relativen Frölicher'schen Spektralsequenz des Morphismus $f$ und auf die lokale Freiheit der Moduln $\\mathrm{R}^qf_*(\\Omega^p_f)$; unsere Ergebnisse können als relative Verallgemeinerungen eines Satzes von Takeo Ohsawa angesehen werden. Im dritten Kapitel unserer Arbeit verwenden wir schließlich die Resultate der beiden vorherigen Kapitel, um einen lokalen Torelli'schen Satz für irreduzibel symplektische komplexe Räume herzuleiten. Als Anwendung des Torelli'schen Satzes zeigen wir, dass irreduzibel symplektische komplexe Räume, deren singulärer Ort eine Kodimension von $4$ oder größer besitzt, der sogenannten Fujiki-Relation genügen."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Bayreuth"],"dc:title":["Irreducible symplectic complex spaces"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Bayreuth"]},"updated_at":"2026-07-27T18:49:06Z"}