47 citations · 270 across the 59 of their papers we have counts for
63 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…
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…
On Universal derivations for multiarrangements
Takuro Abe, Shota Maehara, Gerhard Roehrle +1
The study of universal derivations for arbitrary multiarrangements and multiplicity functions was initiated by Abe, Röhrle, Stump, and Yoshinaga in 2024 which focused on arrangemen…
Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements
Takuro Abe
The Solomon-Terao bi-polynomial was introduced by Solomon and Terao which degenerates to the characteristic polynomial of hyperplane arrangements. Also, it was proved recently that…
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…