| Résume | After giving an overview of known results about stable rationality of hypersurfaces, I will explain an ongoing project with John Christian Ottem to establish several new classes of stably irrational complete intersections. Our results are based on degeneration techniques and a birational version of the nearby cycles functor that was developed in collaboration with Evgeny Shinder. One technique to construct interesting degenerations is the use of tropical geometry; I will demonstrate this technique by proving the stable irrationality of the quartic fivefold. |
