Toric fibrations and models of universal torsors

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dc.contributor.advisorHassett, Brendanen_US
dc.contributor.committeeMemberVarilly-Alvarado, Anthonyen_US
dc.contributor.committeeMemberDobelman, Johnen_US
dc.creatorKozin, Nikitaen_US
dc.date.accessioned2016-03-07T14:41:39Zen_US
dc.date.available2016-03-07T14:41:39Zen_US
dc.date.created2015-05en_US
dc.date.issued2015-04-23en_US
dc.date.submittedMay 2015en_US
dc.date.updated2016-03-07T14:41:40Zen_US
dc.description.abstractWe study smooth projective threefolds fibered by toric surfaces over the projective line. We show that for certain families of degree 6 del Pezzo and quadric surface bundles the universal torsor corresponding to the generic fiber extends to a smooth model over the base. It respects the action of model for the Neron-Severi torus and induces the Abel-Jacobi map from the space of sections. This corresponds to the map from a set of rational points on the generic fiber to the Galois cohomology group of torsors under the Neron-Severi torus. For the model of the latter we also compute corresponding groups of torsors over the base.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationKozin, Nikita. "Toric fibrations and models of universal torsors." (2015) Diss., Rice University. <a href="https://hdl.handle.net/1911/88621">https://hdl.handle.net/1911/88621</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/88621en_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.subjectuniversal torsoren_US
dc.subjectneron modelen_US
dc.subjectalgebraic torusen_US
dc.titleToric fibrations and models of universal torsorsen_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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