A criterion for Lie algebroid connections on a compact Riemann surface

Abstract

Let X be a compact connected Riemann surface and (V,ϕ) a holomorphic Lie algebroid on X such that the holomorphic vector bundle V is stable. We give a necessary and sufficient condition on holomorphic vector bundles E on X to admit a Lie algebroid connection. © The Author(s), under exclusive licence to Springer Nature B.V. 2024.