Kuranishi family of vector bundles and algebraic description of the moduli space of Einstein-Hermitian connections
type: Item
instance of: scholarly article
title: Kuranishi family of vector bundles and algebraic description of the moduli space of Einstein-Hermitian connections
zbMATH Open document ID: 0683.32016
author: Kimio Miyajima
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1989-01-01T00:00:00Z
review text: The main purposes of this paper are to give a complete generalisation of the deformation theory of Kuranishi type for vector bundles and to prove that the differential geometric way and the algebra-geometric way of defining complex structures of the moduli space of irreducible Einstein- Hermitian connections give structures which are isomorphic to each other. Using Banach analytic space arguments the author shows the existence of a semi-universal local family of holomorphic structures and by a power series argument that the obtained family induces that of holomorphic vector bundles. Then he proves that, over a projective algebraic manifold, the analytic moduli space of simple holomorphic structures on a differentiable complex vector bundle \({\mathcal E}\) and the underlying complex space of the moduli space of simple algebraic vector bundles differentiably equivalent to \({\mathcal E}\) are isomorphic to each other. Finally he obtains the isomorphism of the two structures of the moduli space of irreducible Einstein-Hermitian connections and that the forgetful map from this moduli space into that of simple holomorphic structures is an open embedding as not necessarily reduced real analytic spaces.
reviewed by: Sorin Popescu
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 32L05
zbMATH DE Number: 4118711
zbMATH Keywords: simple vector bundle
zbMATH Keywords: moduli space
zbMATH Keywords: irreducible Einstein-Hermitian connections
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195173613
OpenAlex ID: W2088477332
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DOI: 10.2977/PRIMS/1195173613
description: scientific article; zbMATH DE number 4118711