Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 2 (2018), 479-490.
Quadric surface bundles over surfaces and stable rationality
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 , 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.
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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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