Hypersurfaces that are not stably rational

DOI10.1090/JAMS/840zbMATH Open1376.14017arXiv1502.04040OpenAlexW2120832894MaRDI QIDQ2802074

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Publication date: 25 April 2016

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1502.04040

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