Find a geometric interpretation of the nonzero cohomology group

Find a geometric interpretation of the nonzero top-degree cohomology group arising from twisted logarithmic de Rham complexes of multiarrangements.

Background

The paper proves top-degree cohomology concentration for several families of multiarrangements and notes that the resulting cohomology groups sometimes have unexpected extrinsic interpretations. Nevertheless, the authors do not identify a general geometric object or construction whose cohomology is represented by these groups.

A geometric interpretation could explain why top-degree concentration occurs and could connect the algebraic complexes to arrangement complements, local systems, or other geometric structures.

References

Since we do not yet have a geometric interpretation of that cohomology group, we had to develop an algebraic method to prove the cohomology concentration.

— Twisted logarithmic de Rham complexes and the rational hit conjecture  (2610.26028 - Dotsenko, 19 Oct 2026) in Section 1.1, Introduction