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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 ISSN 2199-675X.

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Official URL: https://doi.org/10.1007/s40879-018-0233-1

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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
Dates:
DateEvent
September 2018Published
4 April 2018Available
12 March 2018Accepted
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
Date of first compliant deposit: 14 March 2018
Date of first compliant Open Access: 4 April 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
H98230-16-1-0321National Security Agencyhttp://dx.doi.org/10.13039/100009226
DMS-1601680National Science Foundationhttp://dx.doi.org/10.13039/100000001
14.641.31.0001National Research University Higher School of Economicshttp://dx.doi.org/10.13039/501100007251
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