10 papers
Vector fields of graphic arrangements and face rings of simplicial posets
Takuro Abe, Satoshi Murai
A graphic arrangement $\A_G$ associated with a simple graph is a classical and well-studied object in the theory of hyperplane arrangements. In this note, we show that, for a c…
Residue ideals of hyperplane arrangements
Takuro Abe, Satoshi Murai
In this paper, we introduce a new idea to study modules of logarithmic differential forms of hyperplane arrangements, which we call residue ideals. We first establish basic propert…
Addition theorems for Ziegler pairs of hyperplane arrangements
Takuro Abe, Lukas Kühne, Piotr Pokora
Inspired by Terao's freeness conjecture, we examine Ziegler pairs, which are pairs of hyperplane arrangements that share the same underlying matroid but have different modules of l…
On Ziegler's conjectures for logarithmic derivations of arrangements
Takuro Abe, Graham Denham
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…
Deletion-Restriction for Logarithmic Forms on Multiarrangements
Takuro Abe, Graham Denham
We consider the behaviour of logarithmic differential forms on arrangements and multiarrangements of hyperplanes under the operations of deletion and restriction, extending early w…
On the projective dimension of some deformations of Weyl arrangements
Takuro Abe, Daniele Faenzi
We show that the logarithmic derivation module of (the cone of) the deformation A of a Weyl arrangement associated with a root system of simply laced type has projective dimension…