Satoshi Murai

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4 papers · 1 filter

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 $G$ 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…

math.CO2025

A proof of the Fields Conjectures

Satoshi Murai, Brendon Rhoades, Andy Wilson

The {\em superspace ring} of rank $n$ is the algebra $Ω_{n}$ of differential forms on affine $n$ -space. The algebra $Ω_{n}$ is bigraded with respect to polynomial and exterior degree a…

math.CO2024

Superspace coinvariants and hyperplane arrangements

Robert Angarone, Patricia Commins, Trevor Karn +2

Let $Ω$ be the {\em superspace ring} of polynomial-valued differential forms on affine $n$ -space. The natural action of the symmetric group $S_{n}$ on $n$ -space induces an…