Dokument: Bielliptic surfaces over arbitrary ground fields
| Titel: | Bielliptic surfaces over arbitrary ground fields | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=70570 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20250902-124834-8 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | Kroon, Ivo Daniel [Autor] | |||||||
| Dateien: |
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| Beitragende: | Prof. Dr. Schröer, Stefan [Betreuer/Doktorvater] Prof. Dr. Hornbostel, Jens [Gutachter] | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | Bielliptic surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero.
Over algebraically closed fields every bielliptic surface arises as a quotient of a product of two genus-one curves by a finite commutative group scheme. We study the classification of bielliptic surfaces in an arithmetic setting, i.e.\ over arbitrary ground fields. Our main result states that in this context not every bielliptic surface is a quotient of a product of two curves. This can be attributed to an obstruction in a second cohomology group. We furthermore construct concrete examples of bielliptic surfaces that are not quotients of the above form. | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Algebraische Geometrie | |||||||
| Dokument erstellt am: | 02.09.2025 | |||||||
| Dateien geändert am: | 02.09.2025 | |||||||
| Promotionsantrag am: | 06.02.2025 | |||||||
| Datum der Promotion: | 28.04.2025 |
