Density of rational points on K3 surfaces over function fields

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dc.contributor.advisorHassett, Brendan E.en_US
dc.contributor.committeeMemberWolf, Michaelen_US
dc.contributor.committeeMemberRojo, Javieren_US
dc.creatorLi, Zhiyuanen_US
dc.date.accessioned2012-09-06T04:40:25Zen_US
dc.date.accessioned2012-09-06T04:40:38Zen_US
dc.date.available2012-09-06T04:40:25Zen_US
dc.date.available2012-09-06T04:40:38Zen_US
dc.date.created2012-05en_US
dc.date.issued2012-09-05en_US
dc.date.submittedMay 2012en_US
dc.date.updated2012-09-06T04:40:38Zen_US
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.en_US
dc.format.mimetypeapplication/pdfen_US
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>.en_US
dc.identifier.slug123456789/ETD-2012-05-173en_US
dc.identifier.urihttps://hdl.handle.net/1911/64698en_US
dc.language.isoengen_US
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.en_US
dc.subjectK3 surfacesen_US
dc.subjectSectionsen_US
dc.subjectAbel-Jacobi mapen_US
dc.subjectIntermediate jacobianen_US
dc.subjectNeron modelen_US
dc.subjectCalabi-Yau threefolden_US
dc.titleDensity of rational points on K3 surfaces over function fieldsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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