Stable rationality of hypersurfaces of mock toric variety II

Abstract

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 ${\mathbb{P}}_{\mathbb{C}}^{2n-5}$ is not stably rational, then a very general hypersurface of degree $d$ in ${\mathrm{Gr}}_{\mathbb{C}}(2,n)$ is not stably rational.

40 pages