On the rationality problem for low degree hypersurfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914252690817024 |
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| author | Lange, Jan Schreieder, Stefan |
| author_facet | Lange, Jan Schreieder, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rationality problem for low degree hypersurfaces Lange, Jan Schreieder, Stefan Algebraic Geometry Number Theory 14J70, 14E08, 14M20, 14C25 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. |
| title | On the rationality problem for low degree hypersurfaces |
| topic | Algebraic Geometry Number Theory 14J70, 14E08, 14M20, 14C25 |
| url | https://arxiv.org/abs/2409.12834 |