compact complex manifold, logarithmic connections, Integration on analytic sets and spaces, currents, holomorphic vector bundle, Chern classes, Residues for several complex variables, 32C30, 14C30, Complex manifolds, Characteristic classes and numbers in differential topology, Holomorphic bundles and generalizations, meromorphic connection, residue, Sheaves and cohomology of sections of holomorphic vector bundles, general results, residue formula for Chern classes, holomorphic vector bundle with logarithmic connection, Connections (general theory)