On the rationality problem for hypersurfaces

verfasst von

Jan Lange, Stefan Schreieder

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.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Typ

Preprint

Publikationsdatum

19.09.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)