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

Symmetry Integrability and Geometry-Methods and Applications

article

Indranil Biswas¹  Tomás L. Gómez² 

[1] School of Mathematics, Tata Institute of Fundamental Research;Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Campus Cantoblanco UAM

关键词: Einstein–Hermitian connection;    principal bundle;    parabolic subgroup;    (semi)stability;   

DOI  :  10.3842/SIGMA.2014.013

来源: National Academy of Science of Ukraine

【 摘 要 】

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 E G admits an Einstein-Hermitian connection if and only if E G 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].

【 授权许可】

Unknown