Hassett, Brendan E.2012-09-062012-09-062012-09-062012-09-062012-052012-09-05May 2012Li, 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>.https://hdl.handle.net/1911/64698In 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.application/pdfengCopyright 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.K3 surfacesSectionsAbel-Jacobi mapIntermediate jacobianNeron modelCalabi-Yau threefoldThesis2012-09-06123456789/ETD-2012-05-173