Invariant polynomials on compact complex manifolds
type: Item
instance of: scholarly article
title: Invariant polynomials on compact complex manifolds
zbMATH Open document ID: 0587.32042
author: Akito Futaki
author: Shigeyuki Morita
published in: Proceedings of the Japan Academy. Series A
publication date: 1984-01-01T00:00:00Z
review text: In Invent. Math. 73, 437-443 (1983; Zbl 0506.53030)] the first author introduced a new obstruction for a compact complex manifold M (dim M\(=n)\) with positive \(c_ 1(M)\) to admit a Kähler-Einstein metric. The obstruction is a character \(f: h(M)\to {\mathbb{C}},\) \(h(M)\) being the complex Lie algebra of all holomorphic vector fields of M. In the paper under review the authors interpretate f in terms of secondary characteristic classes of Chern-Simons and Cheeger-Simons. Moreover let H(M) be the complex Lie group of all automorphisms of M and let \(I^ p(G)\) denote the set of all holomorphic G-invariant symmetric polynomials of degree p, for any complex Lie group G; the authors introduce and study a linear map \(F: I^{n+k}(GL(n,{\mathbb{C}}))\to I^ k(H(M))\) which generalizes f, since \(f=F(c_ 1^{n+1})\), up to a constant.
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 3941946
zbMATH Keywords: Lie algebra of holomorphic vector fields
zbMATH Keywords: compact complex manifold
zbMATH Keywords: Kähler-Einstein metric
zbMATH Keywords: G-invariant symmetric polynomials
reviewed by: Cristina Turrini
MaRDI profile type: Publication
full work available at URL: pjaa.60.369
OpenAlex ID: W1990852117
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DOI: 10.3792/PJAA.60.369
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description: scientific article; zbMATH DE number 3941946