Rationality in families of threefolds
Rationality in families of threefolds
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Davide Fusi, University of Utah
In a joint work with Tommaso de Fernex, we prove that in a family of projective threefolds de铿乶ed over an algebraically closed 铿乪ld, the locus of rational 铿乥ers is a countable union of closed subsets of the locus of separably rationally connected 铿乥ers. When the ground 铿乪ld has characteristic zero, this implies that the locus of rational 铿乥ers in a smooth family of projective threefolds is a countable union of closed subsets of the parameter space. General expectation suggests that the result maybe false in higher dimension.