Simen Westbye Moe (Imperial College London) - Stable Rationality of Polytopes

Specialization of (stable) birational types is an important tool when studying (stable) rationality in families. A crucial ingredient is to cook up one parameter degenerations such that the limit has certain combinatorial and geometric properties. Nicaise-Ottem studied these questions for hypersurfaces in algebraic tori, and used tropical geometry to construct degenerations that would have been hard (impossible) to construct geometrically. Even after these are constructed one must carefully study the limit in order to apply specialization techniques, this involves both combinatorics and questions about variation of stable birational types. I will talk about the specialization technique in the setup of Nicaise-Ottem, explain some natural questions that appear through the combinatorics, and give some positive results in this direction.