The motivic nearby fiber and degeneration of stable rationality

Abstract

We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and Lunts for stable rationality in the Grothendieck ring of varieties.

arXiv commentImproved presentation; appendix added with a self-contained construction of the motivic volume based on logarithmic geometry and weak factorization. To appear in Inventiones Mathematicae