On the rationality of some real threefolds
arXiv:2412.13624 · doi:10.1017/S1474748026101613
Abstract
We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian obstructions to rationality vanish. We obtain both negative and positive results, using unramified cohomology and birational rigidity techniques, as well as concrete rationality constructions.
20 pages, final version