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arXiv · 1201.4355

Rationality in families of threefolds

Tommaso de Fernex·Davide Fusi
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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.

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Tommaso de Fernex, Davide Fusi. 2012-05-15. Rationality in families of threefolds. https://arxiv.org/abs/1201.4355

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