Tropical degenerations and stable rationality
John Christian Ottem, Johannes Nicaise · NORA - Norwegian Open Research Archives · 2022
We use the motivic obstruction to stable rationality introduced by Shinder and the first-named author to establish several new classes of stably irrational hypersurfaces and complete intersections. In particular, we show that very general quartic fivefolds and complete intersections of a quadric and a cubic in P6 are stably irrational. An important new ingredient is the use of tropical degeneration techniques.