Local moduli spaces in analytic geometry
type: Item
instance of: scholarly article
title: Local moduli spaces in analytic geometry
zbMATH Open document ID: 0634.32017
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: A graded complex space is a graded \({\mathbb{C}}\)-ringed space (X,\({\mathcal O})\), \({\mathcal O}=\oplus_{k\geq 0}{\mathcal O}_ k\), such that: (X,\({\mathcal O}_ 0)\) is a complex space, \({\mathcal O}\) is an \({\mathcal O}_ 0\)-algebra of finite presentation and each \({\mathcal O}_ k\) is coherent over \({\mathcal O}_ 0\). A very general existence theorem for local moduli spaces in the context of graded complex spaces is presentated in this first paper (to be continued in the following review). This result includes as special cases the existence of local moduli for compact complex spaces, isolated singularities, coherent analytic sheaves with compact supports or isolated singularities, principal bundles over compact complex spaces, as well as the existence of the Douady spaces.
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 32G05
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32K99
zbMATH DE Number: 4032082
zbMATH Keywords: deformation theory
zbMATH Keywords: analytic sheaves
zbMATH Keywords: moduli spaces
zbMATH Keywords: complex spaces
author: Juergen Bingener
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195176447
OpenAlex ID: W1966946196
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DOI: 10.2977/PRIMS/1195176447
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description: scientific article; zbMATH DE number 4032082