Indranil Biswas, "Differential operators and flat connections on a Riemann surface", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 935075, 16 pages, 2003. https://doi.org/10.1155/S0161171203212187
Differential operators and flat connections on a Riemann surface
We consider filtered holomorphic vector bundles on a compact Riemann surface equipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. If is a stable vector bundle of rank and degree , then any holomorphic connection on the jet bundle satisfies this transversality condition for the natural filtration of defined by projections to lower-order jets. The vector bundle admits holomorphic connection. The main result is the construction of a bijective correspondence between the space of all equivalence classes of holomorphic vector bundles on with a filtration of length together with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of order whose symbol is the identity map.
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