Density of rational points on K3 surfaces over function fields

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dc.contributor.advisorHassett, Brendan E.
dc.contributor.committeeMemberWolf, Michael
dc.contributor.committeeMemberRojo, Javier
dc.creatorLi, Zhiyuan
dc.date.accessioned2012-09-06T04:40:25Z
dc.date.accessioned2012-09-06T04:40:38Z
dc.date.available2012-09-06T04:40:25Z
dc.date.available2012-09-06T04:40:38Z
dc.date.created2012-05
dc.date.issued2012-09-05
dc.date.submittedMay 2012
dc.date.updated2012-09-06T04:40:38Z
dc.description.abstractIn 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.mimetypeapplication/pdf
dc.identifier.citationLi, 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.slug123456789/ETD-2012-05-173
dc.identifier.urihttps://hdl.handle.net/1911/64698
dc.language.isoeng
dc.rightsCopyright 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.subjectK3 surfaces
dc.subjectSections
dc.subjectAbel-Jacobi map
dc.subjectIntermediate jacobian
dc.subjectNeron model
dc.subjectCalabi-Yau threefold
dc.titleDensity of rational points on K3 surfaces over function fields
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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