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Density of rational points on K3 surfaces over function fields

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Title: Density of rational points on K3 surfaces over function fields
Author: Li, Zhiyuan
Advisor: Hassett, Brendan E.
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. (2012) "Density of rational points on K3 surfaces over function fields." Doctoral Thesis, Rice University. http://hdl.handle.net/1911/64698.
URI: http://hdl.handle.net/1911/64698
Date: 2012-09-05

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