四次方的对角线

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2023-11-01 DOI:10.14231/ag-2023-027

Nebojsa Pavic, Stefan Schreieder

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引用次数: 2

摘要

我们证明了$\mathbb P^6 $中一个非常一般的四次超曲面在不同于2的特征域上不允许对角线分解，因此它不是缩回有理的。这推广了Nicaise—Ottem的结果，后者在特征为0的域上显示了稳定的无理性。为了证明我们的结果，我们引入了一个新的循环理论障碍，它可以看作是Nicaise- Shinder和Kontsevich- Tschinkel在特征零点引入的理性动机障碍的类似物。

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The diagonal of quartic fivefolds

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.

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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.