Narasimhan-Seshadri connection and Kähler structure of the space of moduli of holomorphic vector bundles over Riemann surfaces
type: Item
instance of: scholarly article
title: Narasimhan-Seshadri connection and Kähler structure of the space of moduli of holomorphic vector bundles over Riemann surfaces
zbMATH Open document ID: 0614.32019
DOI: 10.1007/BF01078478
author: Leon A. Takhtajan
author: Peter Zograf
publication date: 1986-01-01T00:00:00Z
review text: Let \(N=N(n,0)\) be the moduli space of stable vector bundles of rank n and degree 0 over compact Riemann surface S of genus \(g>1\), \(\omega\) is closed (1,1)-form, defining natural Kähler structure on N, and \(A_ E\)- Narasimhan-Seshadri connection, the unique flat unitary connection on a stable vector bundle E of degree 0 over S, compatible with complex structure. The authors show that \(A_ E\) plays in relation to \(\omega\) the same role, as Fuchsian projective connection on S with respect to Weil-Petersson simplectic form on Teichmüller space T(S) [see the authors' paper in Funct. Anal. Appl. 19, 219-220 (1985); translation from Funkts. Appl. Prilozh. 19, No.3, 67-68 (1985; Zbl 0612.31018)], namely, \({\bar \partial}A_ E=-2\sqrt{-1}\omega.\)
reviewed by: Boris N. Apanasov
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 3993974
zbMATH Keywords: moduli space of stable vector bundles
zbMATH Keywords: Narasimhan-Seshadri connection
MaRDI profile type: Publication
cites work: Linear complexes of \(k\)-planes
cites work: Stable and unitary vector bundles on a compact Riemann surface
cites work: Holomorphic vector bundles on a compact Riemann surface
full work available at URL: https://doi.org/10.1007/bf01078478
OpenAlex ID: W1996584123
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3993974