Some low-dimensional hypersurfaces that are not stably rational
Algebraic Geometry
2015-12-23 v4
Abstract
Using Voisin's method we prove that a very general hypersurface of degree at least 4 in complex projective space of dimension 6, 7, 8 or 9 is not stably rational and so, in particular, not rational. We obtain the same conclusion for the double covering of projective space of dimension 6, 7, 8 or 9, branched along a very general quartic hypersurface. On the other hand, such double coverings as well as general quartic hypersurfaces of dimension at least 5 are known to be unirational.
Keywords
Cite
@article{arxiv.1510.02011,
title = {Some low-dimensional hypersurfaces that are not stably rational},
author = {Stefan Schreieder and Luca Tasin},
journal= {arXiv preprint arXiv:1510.02011},
year = {2015}
}
Comments
Paper withdrawn by the authors, due to a major mistake in Prop. 13