2024/06/19 by Taro Yoshino, Yoshino, Taro · 1 citation
Computer Science · Mathematics · #14D06 #14E08 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2407.03354
openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℙ2n-5_ℂ is not stably rational, then a very general hypersurface of degree d in Gr_ℂ(2, n) is not stably rational.