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arXiv · 1502.07581

On small deformations of balanced manifolds

Daniele Angella·Luis Ugarte
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Abstract

We introduce a property of compact complex manifolds under which the existence of balanced metric is stable by small deformations of the complex structure. This property, which is weaker than the $\partial\overline\partial$-Lemma, is characterized in terms of the strongly Gauduchon cone and of the first $\partial\overline\partial$-degree measuring the difference of Aeppli and Bott-Chern cohomologies with respect to the Betti number $b_1$.

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Daniele Angella, Luis Ugarte. 2015-02-26. On small deformations of balanced manifolds. https://doi.org/10.1016/j.difgeo.2017.07.010

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