Stably irrational hypersurfaces of small slopes

TL;DR

This paper proves that very general hypersurfaces of dimension greater than two and sufficiently high degree are not stably rational over the algebraic closure of an uncountable field with characteristic not two.

Contribution

It establishes new bounds on the degree of hypersurfaces that are not stably rational, extending understanding of rationality properties in algebraic geometry.

Findings

Hypersurfaces with degree at least log_2(N)+2 are not stably rational.

The result applies to very general hypersurfaces in characteristic not two.

Provides new insights into the stable rationality of algebraic varieties.

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 $\log_2N +2$ is not stably rational over the algebraic closure of k.