# Rationality in families of threefolds

Tuesday, November 20, 2012 -

4:30pm to 6:00pm

In a joint work with Tommaso de Fernex, 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 a countable union of closed subsets of the parameter space. General expectation suggests that the result maybe false in higher dimension.

Speaker:

Davide Fusi

University of Utah

Event Location:

Fine Hall 322