Stably irrational hypersurfaces of small slopes

Abstract

Let k k be an uncountable field of characteristic different from two. We show that a very general hypersurface X ⊂ P k N + 1 X\subset \mathbb {P}^{N+1}_k of dimension N ≥ 3 N\geq 3 and degree at least log 2 ⁡ N + 2 \log _2N +2 is not stably rational over the algebraic closure of k k .