  In his paper and thesis in 1989, Ziegler posed several conjectures regarding
commutative algebra related to hyperplane arrangements. In this article, we
revisit two of them. One is on generic cuts of free arrangements, and the other
has to do with minimal degree generators for the logarithmic differential
forms. We prove the first one, and disprove the second one. We also give some
positive answers to related problems he posed, using recent developments in
arrangement theory.
