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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146826 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862683401993060352 |
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| author | Biswas, I. Gómez, T.L. |
| author_facet | Biswas, I. Gómez, T.L. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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].
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| first_indexed | 2025-12-07T15:55:56Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146826 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:55:56Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group Biswas, I. Gómez, T.L. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146826 |
| work_keys_str_mv | AT biswasi semistabilityofprincipalbundlesonakahlermanifoldwithanonconnectedstructuregroup AT gomeztl semistabilityofprincipalbundlesonakahlermanifoldwithanonconnectedstructuregroup |