A criterion for Lie algebroid connections on a compact Riemann surface

Abstract

Let $X$ be a compact connected Riemann surface and $(V,\varphi )$ 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.

arXiv commentFinal version; to appear in Geometriae Dedicata