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Non-Kähler Calabi-Yau manifolds

We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly larger. After making some elementary remarks, we show that a manifold in Fujiki's class C with vanishing first Bott-Chern class has torsion canonical bundle. We also give some examples of non-Kahler Calabi-Yau manifolds, and discuss the problem of defining and constructing canonical metrics on them.

preprint2015arXivOpen access
Valentino Tosatti
math.CVmath.AGmath.DG
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Valentino Tosatti

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