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arXiv · 1710.07270

Stable rationality of quadric and cubic surface bundle fourfolds

Asher Auel·Christian Böhning·Alena Pirutka
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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 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.

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Asher Auel, Christian Böhning, Alena Pirutka. 2017-10-19. Stable rationality of quadric and cubic surface bundle fourfolds. https://doi.org/10.1007/s40879-018-0233-1

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