The diagonal of quartic fivefolds

Nebojsa Pavic; Stefan Schreieder

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arXiv · 2106.04539

The diagonal of quartic fivefolds

Nebojsa Pavic·Stefan Schreieder

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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.

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Nebojsa Pavic, Stefan Schreieder. 2021-06-08. The diagonal of quartic fivefolds. https://arxiv.org/abs/2106.04539

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