(Stable) rationality is not deformation invariant

Abstract

We prove the existence of a family $\mathcal{X}\to B$ of smooth projective fourfolds, such that the very general fiber ${\mathcal{X}}_t$ is not stably rational (a fortiori not rational), but some special fibers ${\mathcal{X}}_t$ are rational (a fortiori stably rational).

The paper is withdrawn by the author, who has been informed by A. Beauville that his paper arXiv:1411.3122, on which the present paper heavily depends, has a serious gap

References in corpus (4)

• Hypersurfaces that are not stably rational
• Rationality does not specialize among terminal varieties
• Stable rationality and conic bundles
• Some low-dimensional hypersurfaces that are not stably rational

Cited by in corpus (3)

• Stable rationality of quadric surface bundles over surfaces
• On the rationality of quadric surface bundles
• Some low-dimensional hypersurfaces that are not stably rational