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