On Ziegler's conjectures for logarithmic derivations of arrangements
Combinatorics
2026-05-20 v3 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.2307.08173,
title = {On Ziegler's conjectures for logarithmic derivations of arrangements},
author = {Takuro Abe and Graham Denham},
journal= {arXiv preprint arXiv:2307.08173},
year = {2026}
}
Comments
corrections and revisions with thanks to the referee