Algebra & Number Theory

Quadric surface bundles over surfaces and stable rationality

Stefan Schreieder

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1527040852

Digital Object Identifier
doi:10.2140/ant.2018.12.479

Mathematical Reviews number (MathSciNet)
MR3803711

Zentralblatt MATH identifier
06880896

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

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

Citation

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. https://projecteuclid.org/euclid.ant/1527040852


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