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Stable rationality of quadric and cubic surface bundle fourfolds
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Auel, Asher, Boehning, Christian and Pirutka, Alena (2018) Stable rationality of quadric and cubic surface bundle fourfolds. European Journal of Mathematics, 4 . pp. 732-760. doi:10.1007/s40879-018-0233-1
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Official URL: https://doi.org/10.1007/s40879-018-0233-1
Abstract
We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the specialization method for the Chow group of 0-cycles. Our main result is that a very general hypersurface X of bidegree (2,3) in P2×P3 is not stably rational. Via projections onto the two factors, X→P2 is a cubic surface bundle and X→P3 is a conic bundle, and we analyze the stable rationality problem from both these points of view. Also, we introduce, for any n ≥ 4, new quadric surface bundle fourfolds Xn→P2 with discriminant curve Dn⊂P2 of degree 2n, such that Xn has nontrivial unramified Brauer group and admits a universally CH0-trivial resolution.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Surfaces, Cubic, Hypersurfaces | ||||||||||||
| Journal or Publication Title: | European Journal of Mathematics | ||||||||||||
| Publisher: | Springer | ||||||||||||
| ISSN: | 2199-675X | ||||||||||||
| Official Date: | September 2018 | ||||||||||||
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| Volume: | 4 | ||||||||||||
| Page Range: | pp. 732-760 | ||||||||||||
| DOI: | 10.1007/s40879-018-0233-1 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
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