On Ziegler's conjectures for logarithmic derivations of arrangements
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.
Fields of Study & Subjects
Meromorphic and Entire Functions
Advanced Differential Equations and Dynamical Systems
Advanced Mathematical Identities
Publication details
- Journal / source
- Advances in Applied Mathematics
- Volume
- 179
- Pages
- 103113–103113
- Publication date
- 26 May 2026
- Language
- EN