A very general quartic double fourfold or fivefold is not stably rational

TL;DR

This paper proves that very general quartic double fourfolds and fivefolds are not stably rational, extending the understanding of rationality properties in algebraic geometry.

Contribution

It introduces a new application of Voisin's idea to show non-stable rationality for double covers of projective spaces branched along quartic hypersurfaces.

Findings

Double covers of P^4 branched along quartic hypersurfaces are not stably rational.

Double covers of P^5 branched along quartic hypersurfaces are not stably rational.

The method extends to very general quartic double fourfolds and fivefolds.

Abstract

Applying an idea of C. Voisin, we prove that a double cover of P^4 or P^5 branched along a very general quartic hypersurface is not stably rational.