Stable rationality of quadric and cubic surface bundle fourfolds
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Publication:1999420
DOI10.1007/S40879-018-0233-1zbMATH Open1444.14029arXiv1710.07270OpenAlexW2766371431WikidataQ129955365 ScholiaQ129955365MaRDI QIDQ1999420
Author name not available (Why is that?)
Publication date: 27 June 2019
Published in: (Search for Journal in Brave)
Abstract: We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the degeneration method for the Chow group of 0-cycles. Our main result is that a very general hypersurface X of bidegree (2,3) in P^2 x P^3 is not stably rational. Via projections onto the two factors, X is a cubic surface bundle over P^2 and a conic bundle over P^3, and we analyze the stable rationality problem from both these points of view. This provides another example of a smooth family of rationally connected fourfolds with rational and nonrational fibers. Finally, we introduce new quadric surface bundle fourfolds over P^2 with discriminant curve of any even degree at least 8, having nontrivial unramified Brauer group and admitting a universally CH_0-trivial resolution.
Full work available at URL: https://arxiv.org/abs/1710.07270
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