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
|
PDF
- Publisher Version
161kB |
Official URL: http://www.hindawi.com/journals/ijmms/2003/935075....
Related URL: http://dx.doi.org/10.1155/S0161171203212187
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))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.
Item Type: | Article |
---|---|
Source: | Copyright of this article belongs to Hindawi Publishing Corporation. |
ID Code: | 3640 |
Deposited On: | 18 Oct 2010 10:16 |
Last Modified: | 16 May 2016 14:24 |
Repository Staff Only: item control page