(Stable) rationality is not deformation invariant

Claire Voisin

(Stable) rationality is not deformation invariant

Algebraic Geometry 2015-12-23 v4

Authors: Claire Voisin

Abstract

We prove the existence of a family $\mathcal{X}\rightarrow B$ 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).

Keywords

rational maps

Cite

@article{arxiv.1511.03591,
  title  = {(Stable) rationality is not deformation invariant},
  author = {Claire Voisin},
  journal= {arXiv preprint arXiv:1511.03591},
  year   = {2015}
}

Comments

The paper is withdrawn by the author, who has been informed by A. Beauville that his paper arXiv:1411.3122, on which the present paper heavily depends, has a serious gap

Related papers

View all related →