Details
| Original language | English |
|---|---|
| Pages (from-to) | 754-778 |
| Number of pages | 25 |
| Journal | Algebraic Geometry |
| Volume | 10 |
| Issue number | 6 |
| Early online date | 22 Jun 2023 |
| Publication status | Published - 2023 |
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.
Keywords
- algebraic cycles, hypersurfaces, quartics, rationality, retract rationality
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
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In: Algebraic Geometry, Vol. 10, No. 6, 2023, p. 754-778.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The diagonal of quartic fivefolds
AU - Pavic, Nebojsa
AU - Schreieder, Stefan
N1 - Publisher Copyright: © (2023) All Rights Reserved.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - algebraic cycles
KW - hypersurfaces
KW - quartics
KW - rationality
KW - retract rationality
UR - http://www.scopus.com/inward/record.url?scp=85176351755&partnerID=8YFLogxK
U2 - 10.14231/AG-2023-027
DO - 10.14231/AG-2023-027
M3 - Article
VL - 10
SP - 754
EP - 778
JO - Algebraic Geometry
JF - Algebraic Geometry
SN - 2313-1691
IS - 6
ER -