Rationality in families of threefolds

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 rati...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2013-04, Vol.62 (1), p.127-135
Main Authors: de Fernex, Tommaso, Fusi, Davide
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-013-0110-1