For a connected graph G, the modified logarithmic vector field D_R(A_G) is isomorphic as an R-module to the face ring K[P_G] of an explicitly constructed simplicial poset, yielding new formulas for Hilbert series, local cohomology, projective dimension, and regularity.
Residue ideals of hyperplane arrangements
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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 properties of these ideals, including their radicals and primary decompositions, and obtain applications for freeness of restrictions of arrangements. Then we apply these ideals to the study of modules of logarithmic differential $1$-forms for graphic arrangements. We give an explicit generating set for these modules and find a new connection to cover ideals of graphs studied in combinatorial commutative algebra. As a consequence we establish several new connections between arrangement theory and Stanley--Reisner theory.
fields
math.CO 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Vector fields of graphic arrangements and face rings of simplicial posets
For a connected graph G, the modified logarithmic vector field D_R(A_G) is isomorphic as an R-module to the face ring K[P_G] of an explicitly constructed simplicial poset, yielding new formulas for Hilbert series, local cohomology, projective dimension, and regularity.