Principal Bundles Admitting a Holomorphic Connection
نویسنده
چکیده
LetG be a connected affine algebraic reductive group over C. Let P be a holomorphic principal G bundle on M (i.e. the transition functions of P are holomorphic). Assume that P admits a holomorphic connection D compatible with the holomorphic structure. This means the following : D is a holomorphic 1-form on P with values in the Lie algebra, g, of G, such that D is invariant for the action of G on P , and, when restricted to the fibers of P , this form coincides with the holomorphic Maurer-Cartan form. Using the natural identification of the holomorphic tangent space of P with its real tangent space, the holomorphic connection D gives a G connection on P .
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