Satoshi Murai

collaborators

4 papers

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.CO2026

Superspace coinvariants and hyperplane arrangements

Robert Angarone, Patricia Commins, Trevor Karn +2

Let $I^c ◯$ 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 a…

math.CO2025

A proof of the Fields Conjectures

Satoshi Murai, Brendon Rhoades, Andy Wilson

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