Holomorphic deformations of the Ricci-flat \(\partial \overline{\partial}\)-manifolds (Q296165)

The author considers the problem of constructing globally convergent power series of integrable Beltrami differentials, respectively, a global canonical family of holomorphic top-degree forms on the deformation spaces. Such constructions for Calabi-Yau manifolds were presented in [\textit{K. Liu} et al., Invent. Math. 199, No. 2, 423--453 (2015; Zbl 1318.32017)]. The authors generalize the constructions for the larger class of Ricci flat \(\partial\overline\partial\)-manifolds, by using the iteration method. (Here, a \(\partial\overline\partial\)-manifold is a manifold satisfying the \(\partial\overline\partial\)-Lemma; namely, such that, for every pure-type \(d\)-closed form, the properties of \(d\)-exactness, \(\overline\partial\)-exactness, and \(\partial\overline\partial\)-exactness are equivalent.)