Publikationen (FIS)

The diagonal of quartic fivefolds

authored by
Nebojsa Pavic, Stefan Schreieder
Abstract

We show that a very general quartic hypersurface in 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 zero. 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
Article
Journal
Algebraic Geometry
Volume
10
Pages
754-778
No. of pages
25
ISSN
2313-1691
Publication date
2023
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Algebra and Number Theory, Geometry and Topology
Electronic version(s)
https://arxiv.org/abs/2106.04539 (Access: Open)
https://doi.org/10.14231/AG-2023-027 (Access: Open)
https://doi.org/10.48550/arXiv.2106.04539 (Access: Open)
https://doi.org/10.15488/17555 (Access: Open)