Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group

We investigate principal G-bundles on a compact Kähler manifold, where G is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal G-bundle EG admits an Einstein-Hermitian...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2014
Hauptverfasser: Biswas, I., Gómez, T.L.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146826
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group / I. Biswas, T.L. Gómez // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146826
record_format dspace
spelling Biswas, I.
Gómez, T.L.
2019-02-11T16:35:33Z
2019-02-11T16:35:33Z
2014
Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group / I. Biswas, T.L. Gómez // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53C07; 14F05
DOI:10.3842/SIGMA.2014.013
https://nasplib.isofts.kiev.ua/handle/123456789/146826
We investigate principal G-bundles on a compact Kähler manifold, where G is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal G-bundle EG admits an Einstein-Hermitian connection if and only if EG is polystable. We give an equivalent formulation of the (semi)stability condition. A question is to compare this definition with that of [Gómez T.L., Langer A., Schmitt A.H.W., Sols I., Ramanujan Math. Soc. Lect. Notes Ser., Vol. 10, Ramanujan Math. Soc., Mysore, 2010, 281-371].
We would like to thank B. Conrad and A. Nair for discussions. The first-named author acknowledges the support of the J.C. Bose Fellowship. The second-named author thanks the Tata Institute of Fundamental Research for the hospitality during a visit where part of this work was done. This work was partly funded by the grant MTM2010-17389 and ICMAT Severo Ochoa project SEV-2011-0087 of the Spanish Ministerio de Econom´ıa y Competitividad.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
spellingShingle Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
Biswas, I.
Gómez, T.L.
title_short Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
title_full Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
title_fullStr Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
title_full_unstemmed Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
title_sort semistability of principal bundles on a kähler manifold with a non-connected structure group
author Biswas, I.
Gómez, T.L.
author_facet Biswas, I.
Gómez, T.L.
publishDate 2014
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We investigate principal G-bundles on a compact Kähler manifold, where G is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal G-bundle EG admits an Einstein-Hermitian connection if and only if EG is polystable. We give an equivalent formulation of the (semi)stability condition. A question is to compare this definition with that of [Gómez T.L., Langer A., Schmitt A.H.W., Sols I., Ramanujan Math. Soc. Lect. Notes Ser., Vol. 10, Ramanujan Math. Soc., Mysore, 2010, 281-371].
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146826
citation_txt Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group / I. Biswas, T.L. Gómez // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 12 назв. — англ.
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first_indexed 2025-12-07T15:55:56Z
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