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arXiv · 1502.04040

Hypersurfaces that are not stably rational

Burt Totaro
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Abstract

We show that a wide class of hypersurfaces in all dimensions are not stably rational. Namely, for all d at least about 2n/3, a very general complex hypersurface of degree d in P^{n+1} is not stably rational. The statement generalizes Colliot-Thelene and Pirutka's theorem that very general quartic 3-folds are not stably rational. The result covers all the degrees in which Kollar proved that a very general hypersurface is non-rational, and a bit more. For example, very general quartic 4-folds are not stably rational, whereas it was not even known whether these varieties are rational.

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Burt Totaro. 2015-02-13. Hypersurfaces that are not stably rational. https://arxiv.org/abs/1502.04040

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