Kuranishi family of strongly pseudo-convex domains
Paraphrased from the author's introduction: ``The purpose of this paper is to complete T. Akahori's construction of the semi-universal family of strongly pseudo-convex domains of complex dimension at least 4 [cf. \textit{T. Akahori}, Invent. Math. 68, 317-352 (1982; Zbl 0575.32021), and Math. Ann. 264, 525-535 (1983; Zbl 0575.32022)] in the general deformation theoretic context. In this paper, we will consider deformations of strongly pseudo-convex manifolds and will show that Akahori's canonical family of complex structures on a compact level subset of a strictly pluri-subharmonic exhaustion function induces both the semi-universal family and the formally semi-universal convergent family as above, if the complex dimension of the domain is at least 4.'' Miyajima also considers the case of certain isolated singularities in the complex domain and obtains similar results in this case.
scientific article; zbMATH DE number 902846