Coupled connections on a compact Riemann surface

Biswas, Indranil (2003) Coupled connections on a compact Riemann surface Journal de Mathematiques Pures et Appliques, 82 (1). pp. 1-42. ISSN 0021-7824

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We consider holomorphic differential operators on a compact Riemann surface X whose symbol is an isomorphism. Such a differential operator of order n on a vector bundle E sends E to K⊗nX⊗E, where KX is the holomorphic cotangent bundle. We classify all those holomorphic vector bundles E over X that admit such a differential operator. The space of all differential operators whose symbol is an isomorphism is in bijective correspondence with the collection of pairs consisting of a flat vector bundle E over X and a holomorphic subbundle of E satisfying a transversality condition with respect to the connection.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Coupled Connection; Differential Operator; Grassmann Embedding
ID Code:3603
Deposited On:18 Oct 2010 10:20
Last Modified:18 Oct 2010 10:20

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