Hypersurfaces that are not stably rational
Algebraic Geometry
2015-06-16 v3
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.
Keywords
Cite
@article{arxiv.1502.04040,
title = {Hypersurfaces that are not stably rational},
author = {Burt Totaro},
journal= {arXiv preprint arXiv:1502.04040},
year = {2015}
}
Comments
10 pages; v3: application added: rationality does not specialize among klt varieties. To appear in Journal of the AMS