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.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/64698 |
| Date | 06 September 2012 |
| Creators | Li, Zhiyuan |
| Contributors | Hassett, Brendan |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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