Kuranishi family of strongly pseudo-convex domains
type: Item
instance of: scholarly article
title: Kuranishi family of strongly pseudo-convex domains
zbMATH Open document ID: 0868.32026
author: Kimio Miyajima
published in: Osaka Journal of Mathematics
publication date: 1997-08-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32G05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 902846
zbMATH Keywords: deformation of complex structures
zbMATH Keywords: strongly pseudo-convex domains
reviewed by: Karen R. Pinney
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 902846