Quadric surface bundles over surfaces and stable rationality

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 the projective plane, 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.

13 pages; to appear in Algebra & Number Theory

References in corpus (3)

• Quadric surface bundles over surfaces
• Stable rationality of quadric and cubic surface bundle fourfolds
• Intersections of three quadrics in ${\mathbb{P}}^7$

Cited by in corpus (6)

• Stably irrational hypersurfaces of small slopes
• On the rationality problem for quadric bundles
• Stable rationality of quadric and cubic surface bundle fourfolds
• Symmetric locally free resolutions and rationality problems
• On the rationality of quadric surface bundles
• Brauer groups of involution surface bundles