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arXiv · 2406.15828

Parabolic vector bundles and Lie algebroid connections

David Alfaya·Indranil Biswas·Pradip Kumar·Anoop Singh
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Abstract

Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure over the marked points. An analogue of the Atiyah exact sequence for parabolic Lie algebroids is constructed. For any Lie algebroid whose underlying holomorphic vector bundle is stable, we give a complete characterization of all the parabolic vector bundles that admit a parabolic Lie algebroid connection.

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David Alfaya, Indranil Biswas, Pradip Kumar, Anoop Singh. 2024-06-22. Parabolic vector bundles and Lie algebroid connections. https://doi.org/10.4153/s0008414x25101983

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