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

Abstract

Given a holomorphic Lie algebroid $(V,\varphi )$ 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 $(V,\varphi )$.

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