Stable rationality of hypersurfaces in schön affine varieties
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917919682723840 |
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| author | Yoshino, Taro |
| author_facet | Yoshino, Taro |
| contents | In recent years, there has been a development in approaching rationality problems through the 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 shows the non-stable rationality of a very general hypersurface in projective spaces. In this paper, we extend the result of [Nicaise--Ottem'22] not only for hypersurfaces in algebraic tori but also to those in schön affine varieties. In application, we show the irrationality of certain hypersurfaces in the complex Grassmannian variety Gr(2, n) using the motivic method, which coincides with the result obtained by the same author in the previous research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable rationality of hypersurfaces in schön affine varieties Yoshino, Taro Algebraic Geometry 14E08, 14M25 In recent years, there has been a development in approaching rationality problems through the 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 shows the non-stable rationality of a very general hypersurface in projective spaces. In this paper, we extend the result of [Nicaise--Ottem'22] not only for hypersurfaces in algebraic tori but also to those in schön affine varieties. In application, we show the irrationality of certain hypersurfaces in the complex Grassmannian variety Gr(2, n) using the motivic method, which coincides with the result obtained by the same author in the previous research. |
| title | Stable rationality of hypersurfaces in schön affine varieties |
| topic | Algebraic Geometry 14E08, 14M25 |
| url | https://arxiv.org/abs/2502.08153 |