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arXiv · 1510.02011

Some low-dimensional hypersurfaces that are not stably rational

Stefan Schreieder·Luca Tasin
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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.

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Stefan Schreieder, Luca Tasin. 2015-10-07. Some low-dimensional hypersurfaces that are not stably rational. https://arxiv.org/abs/1510.02011

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