We prove the failure of stable rationality for many smooth well formed weighted hypersurfaces of dimension at least 3. It is in particular proved that a very general smooth well formed Fano weighted hypersurface of index one is not stably rational.
Hypersurfaces that are not stably rational
A very general quartic double fourfold or fivefold is not stably rational
A very general quartic or quintic fivefold is not stably rational
![QR code for arXiv:1709.07748 [math.AG]](http://oss.arxitics.com/images/favicon.svg)