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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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Published in: | Rendiconti del Circolo matematico di Palermo 2013-04, Vol.62 (1), p.127-135 |
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container_title | Rendiconti del Circolo matematico di Palermo |
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creator | de Fernex, Tommaso Fusi, Davide |
description | 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. |
doi_str_mv | 10.1007/s12215-013-0110-1 |
format | article |
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subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics |
title | Rationality in families of threefolds |
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