Stable rationality of quadric surface bundles over surfaces

Abstract

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

24 pages

References in corpus (3)

• (Stable) rationality is not deformation invariant
• Rationality does not specialize among terminal varieties
• Varieties that are not stably rational, zero-cycles and unramified cohomology

Cited by in corpus (6)

• Stably irrational hypersurfaces of small slopes
• Quadric surface bundles over surfaces and stable rationality
• Stable rationality of higher dimensional conic bundles
• Stable rationality of quadric and cubic surface bundle fourfolds
• A very general quartic double fourfold is not stably rational
• Intersections of three quadrics in ${\mathbb{P}}^7$