  We investigate the arrangement of hypersurfaces on a nonsingular varieties
whose associated logarithmic vector bundle is arithmetically Cohen-Macaulay
(for short, aCM), and prove that the projective space is the only smooth
complete intersection with Picard rank one that admits an aCM logarithmic
vector bundle. We also obtain a number of results on aCM logarithmic vector
bundles over several specific varieties. As an opposite situation we
investigate the Torelli-type problem that the logarithmic cohomology determines
the arrangement.
