Intersections of three quadrics in ${\mathbb{P}}^7$

Abstract

We study rationality properties of smooth complete intersections of three quadrics in ${\mathbb{P}}^7$. We exhibit a smooth family of such intersections with both rational and non-rational fibers.

18 pages

References in corpus (7)

• Unirational threefolds with no universal codimension 2 cycle
• Stable rationality of cyclic covers of projective spaces
• On stable rationality of Fano threefolds and del Pezzo fibrations
• Quadric surface bundles over surfaces
• Stable rationality of quadric surface bundles over surfaces
• A very general quartic double fourfold is not stably rational
• Stable rationality of del Pezzo fibrations of low degree over projective spaces

Cited by in corpus (3)

• Quadric surface bundles over surfaces and stable rationality
• Stable rationality of quadric and cubic surface bundle fourfolds
• Brauer groups of involution surface bundles