A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection

David Alfaya; Ashima Bansal; Indranil Biswas; Anoop Singh

A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection

Algebraic Geometry 2026-04-30 v1 Differential Geometry

Authors: David Alfaya , Ashima Bansal , Indranil Biswas , Anoop Singh

Abstract

Given a holomorphic Lie algebroid $(V, \phi)$ on a compact connected Riemann surface $X$ , we give a necessary and sufficient condition for a parabolic vector bundle on $X$ , with parabolic structure over a nonzero reduced effective divisor, to admit a parabolic Lie algebroid connection for the Lie algebroid $(V, \phi)$ .

Keywords

parabolic vector bundle Lie algebroid holomorphic connection Riemann surface parabolic structure

Cite

@article{arxiv.2604.26270,
  title  = {A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection},
  author = {David Alfaya and Ashima Bansal and Indranil Biswas and Anoop Singh},
  journal= {arXiv preprint arXiv:2604.26270},
  year   = {2026}
}

Comments

20 pages. arXiv admin note: text overlap with arXiv:2406.15828

A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection

Abstract

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