# Hypersurface arrangements of aCM type

## TL;DR

This paper studies hypersurface arrangements on smooth varieties with arithmetically Cohen-Macaulay logarithmic bundles, proving projective space's uniqueness in certain cases and exploring Torelli-type problems for these bundles.

## Contribution

It demonstrates that projective space is uniquely characterized among smooth complete intersections with Picard rank one by having an aCM logarithmic bundle, and explores related Torelli problems.

## Key findings

- Projective space is the only such smooth complete intersection with an aCM bundle.
- Results on aCM bundles over specific varieties.
- Investigation of Torelli-type problems for logarithmic cohomology.

## 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.