Hypersurface arrangements of aCM type

Abstract

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.