On Ziegler's conjectures for logarithmic derivations of arrangements

Fuente: arXiv
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Autori principali: Abe, Takuro, Denham, Graham
Natura: Preprint
Pubblicazione: 2023
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author Abe, Takuro
Denham, Graham
author_facet Abe, Takuro
Denham, Graham
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_08173
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On Ziegler's conjectures for logarithmic derivations of arrangements
Abe, Takuro
Denham, Graham
Combinatorics
Commutative Algebra
32S22, 52C35
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.
title On Ziegler's conjectures for logarithmic derivations of arrangements
topic Combinatorics
Commutative Algebra
32S22, 52C35
url https://arxiv.org/abs/2307.08173