{"id":{"repo_id":"bayreuth","oai_identifier":"oai:epub.uni-bayreuth.de:440"},"canonical_url":"https://search.dev.ndltd.org/etd/bayreuth/oai:epub.uni-bayreuth.de:440","repository":{"repo_id":"bayreuth","name":"Universität Bayreuth","base_url":"https://epub.uni-bayreuth.de/cgi/oai2"},"display":{"title":"Surfaces Isogenous to a Product: Their Automorphisms and Degenerations","abstract":"In this thesis, I consider the automorphisms and stable degenerations of surfaces isogenous to a product. First I consider the action of the automorphisms on cohomology in the case where the group G is abelian. It is shown that, if the irregularity of the surface is larger than 1, the action of G on the second cohomology is mostly faithful. For surfaces with irregularity 0 or 1, examples are given. Then I consider the stable degenerations of surfaces isogenous to a product and classify the possible singularities on them. As a result, I show that the Q-Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.","abstract_html":"In this thesis, I consider the automorphisms and stable degenerations of surfaces isogenous to a product. First I consider the action of the automorphisms on cohomology in the case where the group G is abelian. It is shown that, if the irregularity of the surface is larger than 1, the action of G on the second cohomology is mostly faithful. For surfaces with irregularity 0 or 1, examples are given. Then I consider the stable degenerations of surfaces isogenous to a product and classify the possible singularities on them. As a result, I show that the Q-Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.","abstract_has_math":false,"creators":["Liu, Wenfei"],"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":2010,"date_issued":"2010-03-12","date_published":"2010-03-12","updated_at":"2026-07-27T18:49:12Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://epub.uni-bayreuth.de/id/eprint/440/","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":["Liu, Wenfei"]}]},{"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 this thesis, I consider the automorphisms and stable degenerations of surfaces isogenous to a product. First I consider the action of the automorphisms on cohomology in the case where the group G is abelian. It is shown that, if the irregularity of the surface is larger than 1, the action of G on the second cohomology is mostly faithful. For surfaces with irregularity 0 or 1, examples are given. Then I consider the stable degenerations of surfaces isogenous to a product and classify the possible singularities on them. As a result, I show that the Q-Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.","In dieser Dissertation betrachten wir Wirkung der Automorphismengruppen von Flächen isogen zu einem Produkt auf der Kohomologie, und stabile Degeneration von solchen Flächen. Wir bemerken, dass es eine starke Beziehung zwischen Automorphismen und der Existenz von feinen Modulräumen gibt, und zwischen Degenerationen und Kompaktifizierungen von Modulräumen von Flächen mit kanonischen Singularitäten auch. Im Fall, dass die Irregularität q(S)>1 ist und G ist abelsch, zeigen wir, dass die Wirkung von G auf der zweiten Kohomologiegruppe meistens effektiv ist. Wir klassifizieren alle möglichen Singularitäten auf diesen stabilen Degenerationen. Als weitere Ergebnisse können wir zeigen, dass die Deformationen von den Degenerationen mit besonderen Singularitäten ohne Obstruktionen sind, und wir bekommen einige Zusammenhängskomponenten des Modulraums von stabilen Flächen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Surfaces Isogenous to a Product: Their Automorphisms and Degenerations"]}]}],"canonical_facts":{"dc:contributor":["Catanese, Fabrizio"],"dc:creator":["Liu, Wenfei"],"dc:description.abstract":["In this thesis, I consider the automorphisms and stable degenerations of surfaces isogenous to a product. First I consider the action of the automorphisms on cohomology in the case where the group G is abelian. It is shown that, if the irregularity of the surface is larger than 1, the action of G on the second cohomology is mostly faithful. For surfaces with irregularity 0 or 1, examples are given. Then I consider the stable degenerations of surfaces isogenous to a product and classify the possible singularities on them. As a result, I show that the Q-Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.","In dieser Dissertation betrachten wir Wirkung der Automorphismengruppen von Flächen isogen zu einem Produkt auf der Kohomologie, und stabile Degeneration von solchen Flächen. Wir bemerken, dass es eine starke Beziehung zwischen Automorphismen und der Existenz von feinen Modulräumen gibt, und zwischen Degenerationen und Kompaktifizierungen von Modulräumen von Flächen mit kanonischen Singularitäten auch. Im Fall, dass die Irregularität q(S)>1 ist und G ist abelsch, zeigen wir, dass die Wirkung von G auf der zweiten Kohomologiegruppe meistens effektiv ist. Wir klassifizieren alle möglichen Singularitäten auf diesen stabilen Degenerationen. Als weitere Ergebnisse können wir zeigen, dass die Deformationen von den Degenerationen mit besonderen Singularitäten ohne Obstruktionen sind, und wir bekommen einige Zusammenhängskomponenten des Modulraums von stabilen Flächen."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Bayreuth"],"dc:title":["Surfaces Isogenous to a Product: Their Automorphisms and Degenerations"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Bayreuth"]},"updated_at":"2026-07-27T18:49:12Z"}