no. 1
Smooth weighted hypersurfaces that are not stably rational
[Hypersurfaces pondérées lisses qui ne sont pas stablement rationnelles]
Okada, Takuzo1
1 Saga University Department of mathematics Faculty of science and Engineering 1 Honjo-machi Saga 840-8502 (Japan)
Annales de l'Institut Fourier, Tome 71 (2021) no. 1, pp. 203-237.

Nous prouvons l’absence rationalité stable pour de nombreuses hypersurfaces pondérées lisses de dimension au moins 3. Il est en particulier prouvé qu’une hypersurface pondérée de Fano très générale lisse de l’indice un n’est pas stablement rationnelle.

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.

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DOI : 10.5802/aif.3390
Classification : 14E08, 14J45, 14J70
Keywords: Fano variety, stable rationality, weighted hypersurface
Mot clés : variété de Fano, rationalité stable, hypersurface pondérée
Okada, Takuzo 1

1 Saga University Department of mathematics Faculty of science and Engineering 1 Honjo-machi Saga 840-8502 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Okada, Takuzo. Smooth weighted hypersurfaces  that are not stably rational. Annales de l'Institut Fourier, Tome 71 (2021) no. 1, pp. 203-237. doi : 10.5802/aif.3390. https://aif.centre-mersenne.org/articles/10.5802/aif.3390/

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