Toric fibrations and models of universal torsors

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dc.contributor.advisorHassett, Brendan
dc.contributor.committeeMemberVarilly-Alvarado, Anthony
dc.contributor.committeeMemberDobelman, John
dc.creatorKozin, Nikita
dc.date.accessioned2016-03-07T14:41:39Z
dc.date.available2016-03-07T14:41:39Z
dc.date.created2015-05
dc.date.issued2015-04-23
dc.date.submittedMay 2015
dc.date.updated2016-03-07T14:41:40Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/88621
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.subjectuniversal torsor
dc.subjectneron model
dc.subjectalgebraic torus
dc.titleToric fibrations and models of universal torsors
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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