Publication Date:
2003-01-01
Description:
We consider filtered holomorphic vector bundles on a compact Riemann surfaceXequipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. IfQis a stable vector bundle of rankrand degree(1−genus(X))nr, then any holomorphic connection on the jet bundleJn(Q)satisfies this transversality condition for the natural filtration ofJn(Q)defined by projections to lower-order jets. The vector bundleJn(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 onXwith a filtration of lengthntogether with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of ordernwhose symbol is the identity map.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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