On the rationality problem for hypersurfaces

Publikation: Arbeitspapier/Preprint › Preprint

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  • Jan Lange
  • Stefan Schreieder

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OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 19 Sept. 2024

Abstract

We show that a very general hypersurface of degree d at least 4 and dimension at most $(d+1)2^{d-4}$ over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor $\mathbb{A}^1$-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.

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On the rationality problem for hypersurfaces. / Lange, Jan; Schreieder, Stefan.
2024.

Publikation: Arbeitspapier/Preprint › Preprint

Lange, J & Schreieder, S 2024 'On the rationality problem for hypersurfaces'.
Lange, J., & Schreieder, S. (2024). On the rationality problem for hypersurfaces. Vorabveröffentlichung online.
Lange J, Schreieder S. On the rationality problem for hypersurfaces. 2024 Sep 19. Epub 2024 Sep 19.
Lange, Jan ; Schreieder, Stefan. / On the rationality problem for hypersurfaces. 2024.
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