Year: 2026
Type: preprint
Abstract: We prove that a very general hypersurface of degree at least five and any positive dimension does not have a decomposition of the diagonal, over an uncountable algebraically closed field of characteristic not $2$. In particular, such hypersurfaces are not stably or retract rational. For the proof, we construct (in each dimension $\geq 8$) a certain quintic hypersurface with a nonzero unramified cohomology class, and which is rationally fibered by quadrics over a lower-dimensional projective space. From our construction, the main result follows using methods developed by Schreieder.
Source: arXiv (Cornell University)
Author: Hotchkiss, James
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221041241