# On small deformations of balanced manifolds

created by stoppato on 08 Nov 2016
modified by daniele on 24 Dec 2017

[BibTeX]

Published Paper

Inserted: 8 nov 2016
Last Updated: 24 dec 2017

Journal: Differ. Geom. Appl.
Volume: 54
Number: Part B
Pages: 464-474
Year: 2017

ArXiv: 1502.07581 PDF
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 $b_1$.