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principal bundles in differential geometry is a classical notion and there are so many references that discuss these notion (even in text books). But, when it comes to its version in complex geometry, namely holomorphic principal bundles over complex manifolds, there does not seem to be much literature.

There are some papers devoted to holomorphic principal bundle when the base has some extra properties (Riemann surfaces, complex projective varieties, and so on), but I am not able to find much literature for a holomorphic principal bundle over an arbitrary complex manifolds.

Are there references that discusses the general notion: holomorphic principal bundles over complex manifolds? If there are any, please provide details.

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    $\begingroup$ For some results, once the case of vector bundles is handled, the case of principal bundles is easy. For example for the nonabelian Hodge correspondence this is discussed by Carlos Simpson in his paper "Higgs bundles and local systems". $\endgroup$
    – Will Sawin
    Commented May 27, 2022 at 18:34
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    $\begingroup$ @WillSawin can you suggest some references where I can see some details about holomorphic principal bundles... $\endgroup$
    – Praphulla Koushik
    Commented May 28, 2022 at 2:23
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    $\begingroup$ You could also try to search holomorphic torsors? $\endgroup$
    – Z. M
    Commented May 28, 2022 at 8:26
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    $\begingroup$ @Z.M Not many results are coming for holomorphic torsors... If you have any specific reference in mind, please share.. $\endgroup$
    – Praphulla Koushik
    Commented May 29, 2022 at 3:46
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    $\begingroup$ @MoisheKohan my question was related to principal bundles..so, I mentioned that, Kobayashi reference does not say manythings about principal bundles, so, not really useful for this situation.. $\endgroup$
    – Praphulla Koushik
    Commented Jun 4, 2022 at 14:28

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