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- Title
The diagonal of quartic fivefolds.
- Authors
Pavic, Nebojsa; Schreieder, Stefan
- Abstract
We show that a very general quartic hypersurface in P6k 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.
- Subjects
QUARTIC surfaces; HYPERSURFACES; DECOMPOSITION method; THEORY of retracts; TOPOLOGY
- Publication
Algebraic Geometry, 2023, Vol 10, Issue 6, p754
- ISSN
2313-1691
- Publication type
Article
- DOI
10.14231/ag-2023-027