A Criterion for Flatness of Sections of Adjoint Bundle of a Holomorphic Principal Bundle over a Riemann Surface
نویسندگان
چکیده
Let EG be a holomorphic principal G–bundle over a compact connected Riemann surface, where G is a connected reductive affine algebraic group defined over C, such that EG admits a holomorphic connection. Take any β ∈ H(X, ad(EG)), where ad(EG) is the adjoint vector bundle for EG, such that the conjugacy class β(x) ∈ g/G, x ∈ X , is independent of x. We give a sufficient condition for the existence of a holomorphic connection on EG such that β is flat with respect to the induced connection on ad(EG). 2010 Mathematics Subject Classification: 14H60, 14F05, 53C07
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