International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 935075 | https://doi.org/10.1155/S0161171203212187

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

Received21 Dec 2002

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 (1genus(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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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