Differential operators and flat connections on a Riemann surface

Biswas, Indranil (2003) Differential operators and flat connections on a Riemann surface International Journal of Mathematics and Mathematical Sciences, 64 . pp. 4041-4056. ISSN 0161-1712

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Official URL: http://www.hindawi.com/journals/ijmms/2003/935075....

Related URL: http://dx.doi.org/10.1155/S0161171203212187


We consider filtered holomorphic vector bundles on a compact Riemann surface X equipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. If Q is a stable vector bundle of rank r and degree (1-genus(X))nr, then any holomorphic connection on the jet bundle Jn(Q) satisfies this transversality condition for the natural filtration of Jn(Q) defined by projections to lower-order jets. The vector bundle Jn(Q) 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 X with a filtration of length n together with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of order n whose symbol is the identity map.

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Deposited On:18 Oct 2010 10:16
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