The Hodge decomposition for some non-Kahler threefolds with trivial canonical bundle.

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Robert Friedman, Columbia University
Fine Hall 322

We show that the \partial\bar{\partial}-lemma holds for the non-Kahler compact complex manifolds of dimension three with trivial canonical bundle constructed by Clemens as deformations of Calabi-Yau threefolds contracted along smooth rational curves with normal bundle of type (-1, -1), at least on an open dense set in moduli. The  proof uses the mixed Hodge structure on the singular fibers and an analysis of the variation of the Hodge filtration for the smooth fibers.