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Workshop on birational geometry
November 10, 2021 15:30–16:30, HSE University, Laboratory of Algebraic Geometry and Its Applications, online
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The diagonal of quartic fivefolds
S. Schreieder |
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This page: | 57 |
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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 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. This is joint work with Nebojsa Pavic.
Language: English
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