Quadric surface bundles over surfaces and stable rationality

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Stefan Schreieder

External Research Organisations

  • Ludwig-Maximilians-Universität München (LMU)
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Details

Original languageEnglish
Pages (from-to)479-490
Number of pages12
JournalAlgebra and Number Theory
Volume12
Issue number2
Publication statusPublished - 13 May 2018
Externally publishedYes

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.

Keywords

    Brauer group, Decomposition of the diagonal, Lüroth problem, Rationality problem, Stable rationality, Unramified cohomology

ASJC Scopus subject areas

Cite this

Quadric surface bundles over surfaces and stable rationality. / Schreieder, Stefan.
In: Algebra and Number Theory, Vol. 12, No. 2, 13.05.2018, p. 479-490.

Research output: Contribution to journal › Article › Research › peer review

Schreieder S. Quadric surface bundles over surfaces and stable rationality. Algebra and Number Theory. 2018 May 13;12(2):479-490. doi: 10.2140/ant.2018.12.479
Schreieder, Stefan. / Quadric surface bundles over surfaces and stable rationality. In: Algebra and Number Theory. 2018 ; Vol. 12, No. 2. pp. 479-490.
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