Algebra & Number Theory

Quadric surface bundles over surfaces and stable rationality

Stefan Schreieder

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We prove a general specialization theorem which implies stable irrationality for a wide class of quadric surface bundles over rational surfaces. As an application, we solve, with the exception of two cases, the stable rationality problem for any very general complex projective quadric surface bundle over 2, given by a symmetric matrix of homogeneous polynomials. Both exceptions degenerate over a plane sextic curve, and the corresponding double cover is a K3 surface.

Article information

Algebra Number Theory, Volume 12, Number 2 (2018), 479-490.

Received: 24 June 2017
Revised: 8 November 2017
Accepted: 18 December 2017
First available in Project Euclid: 23 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E08: Rationality questions [See also 14M20] 14M20: Rational and unirational varieties [See also 14E08]
Secondary: 14J35: $4$-folds 14D06: Fibrations, degenerations

rationality problem stable rationality decomposition of the diagonal unramified cohomology Brauer group Lüroth problem


Schreieder, Stefan. Quadric surface bundles over surfaces and stable rationality. Algebra Number Theory 12 (2018), no. 2, 479--490. doi:10.2140/ant.2018.12.479.

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