On the rationality problem for low degree hypersurfaces

Abstract

We show that a very general hypersurface of degree d at least 4 and dimension at most $(d+1)2^{d-4}$ over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor ${\mathbb{A}}^1$-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.

40 pages, final version, to appear in Forum of Mathematics, Pi

References in corpus (7)

• Unirational threefolds with no universal codimension 2 cycle
• Stably irrational hypersurfaces of small slopes
• On the rationality problem for quadric bundles
• Torsion orders of complete intersections
• Erratum to: Birationally rigid hypersurfaces
• Torsion order of smooth projective surfaces
• Torsion orders of Fano hypersurfaces