Density of rational points on K3 surfaces over function fields
dc.contributor.advisor | Hassett, Brendan E. | |
dc.contributor.committeeMember | Wolf, Michael | |
dc.contributor.committeeMember | Rojo, Javier | |
dc.creator | Li, Zhiyuan | |
dc.date.accessioned | 2012-09-06T04:40:25Z | |
dc.date.accessioned | 2012-09-06T04:40:38Z | |
dc.date.available | 2012-09-06T04:40:25Z | |
dc.date.available | 2012-09-06T04:40:38Z | |
dc.date.created | 2012-05 | |
dc.date.issued | 2012-09-05 | |
dc.date.submitted | May 2012 | |
dc.date.updated | 2012-09-06T04:40:38Z | |
dc.description.abstract | In this paper, we study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the NĀ“eron-Severi group generated by these sections is not finitely generated. This also gives examples of K3 surfaces over the function field F of a complex curve with Zariski dense F-rational points, whose geometric models are Calabi-Yau. Furthermore, we also generalize our results to the cases of families of higher dimensional Calabi-Yau varieties with Calabi-Yau ambient spaces. | |
dc.format.mimetype | application/pdf | |
dc.identifier.citation | Li, Zhiyuan. "Density of rational points on K3 surfaces over function fields." (2012) Diss., Rice University. <a href="https://hdl.handle.net/1911/64698">https://hdl.handle.net/1911/64698</a>. | |
dc.identifier.slug | 123456789/ETD-2012-05-173 | |
dc.identifier.uri | https://hdl.handle.net/1911/64698 | |
dc.language.iso | eng | |
dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | |
dc.subject | K3 surfaces | |
dc.subject | Sections | |
dc.subject | Abel-Jacobi map | |
dc.subject | Intermediate jacobian | |
dc.subject | Neron model | |
dc.subject | Calabi-Yau threefold | |
dc.title | Density of rational points on K3 surfaces over function fields | |
dc.type | Thesis | |
dc.type.material | Text | |
thesis.degree.department | Mathematics | |
thesis.degree.discipline | Natural Sciences | |
thesis.degree.grantor | Rice University | |
thesis.degree.level | Doctoral | |
thesis.degree.name | Doctor of Philosophy |