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math.CO2026
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…
math.CO2026
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…