Stable rationality of hypersurfaces of mock toric variety II

In recent years, there has been a development in approaching rationality problems through motivic methods (cf. Kontsevich--Tschinkel'19, Nicaise--Shinder'19, Nicaise--Ottem'21). This method requires the explicit construction of degeneration families of curves with favorable properties. While the specific construction is generally difficult, Nicaise--Ottem'22 combines combinatorial methods to construct degeneration families of hypersurfaces in toric varieties and mentions the stable rationality of a very general hypersurface in projective spaces. In this paper, we substitute mock toric varieties for toric varieties and we prove the following theorem from the motivic method: If a very general hypersurface of degree d in P^2n-5C is not stably rational, then a very general hypersurface of degree d in GrC (2, n) is not stably rational.