3 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 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 is the algebra of differential forms on affine -space. The algebra is bigraded with respect to polynomial and exterior degree a…