Stably irrational hypersurfaces of small slopes

Abstract

Let k be an uncountable field of characteristic different from two. We show that a very general hypersurface of dimension N>2 and degree at least ${\log }_{2}N+2$ is not stably rational over the algebraic closure of k.

34 pages; Appendix with explicit equations added. To appear in Journal of the AMS

References in corpus (2)

• On the rationality problem for quadric bundles
• Quadric surface bundles over surfaces and stable rationality

Cited by in corpus (5)

• On the integral Hodge conjecture for real varieties, I
• Fano hypersurfaces with arbitrarily large degrees of irrationality
• Torsion orders of Fano hypersurfaces
• On the rationality problem for low degree hypersurfaces
• On the failure of the integral Hodge/Tate conjecture for products with projective hypersurfaces