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arXiv · 2409.12834

On the rationality problem for low degree hypersurfaces

Jan Lange·Stefan Schreieder
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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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Jan Lange, Stefan Schreieder. 2024-09-19. On the rationality problem for low degree hypersurfaces. https://doi.org/10.1017/fmp.2025.10016

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