14 citations · 53 across the 14 of their papers we have counts for
4 papers · 1 filter
Conic bundles with nontrivial unramified Brauer group over threefolds
Asher Auel, Christian Böhning, Hans-Christian Graf v. Bothmer +1
We derive a formula for the unramified Brauer group of a general class of rationally connected fourfolds birational to conic bundles over smooth threefolds. We produce new examples…
A very general quartic double fourfold is not stably rational
Brendan Hassett, Alena Pirutka, Yuri Tschinkel
We prove that a very general double cover of the projective four-space, ramified in a quartic threefold, is not stably rational.
Stable rationality of quadric surface bundles over surfaces
Brendan Hassett, Alena Pirutka, Yuri Tschinkel
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,…
Varieties that are not stably rational, zero-cycles and unramified cohomology
Alena Pirutka
This is a survey of recent examples of varieties that are not stably rational. We review the specialization method based on properties of the Chow group of zero-cycles used in thes…