Existence of holomorphic Lie algebroid connections in higher dimensions

Abstract

Let $(V,\varphi )$ be a holomorphic Lie algebroid over an irreducible smooth complex projective variety $X$ of dimension at least three, and let $E$ be a holomorphic vector bundle on $X$. We establish a necessary and sufficient condition for the existence of a holomorphic $(V,\varphi )$--connection on $E$.

9 pages