The diagonal of quartic fivefolds

authored by

Nebojsa Pavic, Stefan Schreieder

Abstract

We show that a very general quartic hypersurface in \(\mathbb P^6 \) over a field of characteristic different from 2 does not admit a decomposition of the diagonal, hence is not retract rational. This generalizes a result of Nicaise--Ottem, who showed stable irrationality over fields of characteristic 0. To prove our result, we introduce a new cycle-theoretic obstruction that may be seen as an analogue of the motivic obstruction for rationality in characteristic zero, introduced by Nicaise--Shinder and Kontsevich--Tschinkel.

Organisation(s)

Institute of Algebraic Geometry

Type

Preprint

Publication date

22.06.2023

Publication status

E-pub ahead of print

Electronic version(s)

https://arxiv.org/abs/2106.04539 (Access: Open)