The ∂∂-lemma for general Clemens manifolds

2017/08/02 by Friedman, Robert
#14J32 #32G20 #32J17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.00828

Abstract

We show that the ∂∂-lemma holds for the non-Kähler 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.

Related

• Polarized Hodge Structures for Clemens Manifolds
• Clemens' conjecture: part I
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• ∂∂-complex symplectic and Calabi-Yau manifolds: Albanese map, deformations and period maps
• Finite distance problem on the moduli of non-Kähler Calabi--Yau ∂∂-threefolds