Differential operators and flat connections on a Riemann surface

Indranil Biswas

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-16

Abstract:

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 ) ) n r , then any holomorphic connection on the jet bundle J n ( Q ) satisfies this transversality condition for the natural filtration of J n ( Q ) defined by projections to lower-order jets. The vector bundle J n ( 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:935075

DOI: 10.1155/S0161171203212187

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