The $\partial\bar{\partial}$-lemma for general Clemens manifolds
Algebraic Geometry
2020-03-17 v3
Abstract
We show that the -lemma holds for the non-K\"ahler 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 , 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.
Cite
@article{arxiv.1708.00828,
title = {The $\partial\bar{\partial}$-lemma for general Clemens manifolds},
author = {Robert Friedman},
journal= {arXiv preprint arXiv:1708.00828},
year = {2020}
}
Comments
Added Remark 1.3(iii) together with additional references. To appear in PAMQ