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Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
Інший ID:
2010 Mathematics Subject Classification: 53C07; 14F05
DOI:10.3842/SIGMA.2014.013
DOI:10.3842/SIGMA.2014.013
Посилання:
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.
Підтримка:
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.
Дата:
2014
Переглядів:
447
Завантажень:
226
Анотація:
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].
