|
Title:
|
Density of rational points on K3 surfaces over function fields |
|
Author:
|
Li, Zhiyuan |
|
Advisor:
|
Hassett, Brendan |
|
Degree:
|
Doctor of Philosophy thesis |
|
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 N´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. |
|
Citation:
|
Li, Zhiyuan. "Density of rational points on K3 surfaces over function fields." Doctoral Thesis, Rice University, May, 2012. ETD http://hdl.handle.net/1911/64698. |
|
Citable link to this page:
|
http://hdl.handle.net/1911/64698 |
|
Date:
|
2012-09-05 |
