2012/01/20 by de Fernex, Tommaso, Fusi, Davide · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1201.4355
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.