Algebra & Number Theory

Quadric surface bundles over surfaces and stable rationality

Stefan Schreieder

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 $ℙ2$, 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
Revised: 8 November 2017
Accepted: 18 December 2017
First available in Project Euclid: 23 May 2018

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

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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