Hassett, Brendan2016-03-072016-03-072015-052015-04-23May 2015Kozin, 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>.https://hdl.handle.net/1911/88621We 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.application/pdfengCopyright 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.universal torsorneron modelalgebraic torusThesis2016-03-07