Summary:
Given a holomorphic Lie algebroid on an m-pointed connected Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure over the marked points. An analog 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.
Spanish layman's summary:
Definimos conexiones parabólicas sobre algebroides de Lie y hallamos un análogo de la sucesión de Atiyah para algebroides de Lie parabólicos. Para cualquier algebroide de Lie con fibrado estable caracterizamos todos los fibrados parabólicos que admiten una conexión parabólica para el algebroide.
English layman's summary:
We define parabolic Lie algebroid connections and construct an analogue of the Atiyah sequence for parabolic Lie algebroids. For any Lie algebroid with a stable underlying bundle, we give a complete characterization of all the parabolic vector bundles that admit a parabolic Lie algebroid connection.
Keywords: Parabolic bundle; Lie algebroid connection; Atiyah exact sequence; stable bundle; Fibrado parabólico, conexiones sobre algebroides de Lie, sucesión exacta de Atiyah, fibrado estable.
JCR-JIF Impact Factor and WoS quartile: 0,600 - Q3 (2025)
DOI reference:
https://doi.org/10.4153/S0008414X25101983
In press: December 2025.
Citation:
D. Alfaya, I. Biswas, P. Kumar, A. Singh, "Parabolic vector bundles and Lie algebroid connections", Canadian Journal of Mathematics, doi: 10.4153/S0008414X25101983
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