English

Rationality in families of threefolds

Algebraic Geometry 2012-05-16 v2

Abstract

We prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of separably rationally connected fibers. When the ground field has characteristic zero, this implies that the locus of rational fibers in a smooth family of projective threefolds is the union of at most countably many closed subfamilies.

Keywords

Cite

@article{arxiv.1201.4355,
  title  = {Rationality in families of threefolds},
  author = {Tommaso de Fernex and Davide Fusi},
  journal= {arXiv preprint arXiv:1201.4355},
  year   = {2012}
}

Comments

9 pages; v2: minor changes, final version to appear in Rend. Circ. Mat. Palermo