Details
Original language | English |
---|---|
Publication status | E-pub ahead of print - 19 Sept 2024 |
Abstract
Keywords
- math.AG, math.NT, 14J70, 14E08, 14M20, 14C25
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
2024.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - On the rationality problem for hypersurfaces
AU - Lange, Jan
AU - Schreieder, Stefan
N1 - 37 pages
PY - 2024/9/19
Y1 - 2024/9/19
N2 - 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.
AB - 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.
KW - math.AG
KW - math.NT
KW - 14J70, 14E08, 14M20, 14C25
M3 - Preprint
BT - On the rationality problem for hypersurfaces
ER -