On the rationality of some real threefolds

TL;DR

This paper investigates the rationality of certain real threefolds, specifically conic and quadric surface bundles, using advanced cohomological and birational methods, providing both positive and negative results.

Contribution

It offers new insights into the rationality problem for real threefolds, combining unramified cohomology, birational rigidity, and explicit constructions.

Findings

Identifies conditions under which these threefolds are rational or non-rational.

Provides explicit examples demonstrating both rationality and non-rationality.

Uses advanced techniques to analyze the real locus and intermediate Jacobian obstructions.

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.