Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one

2022/06/30 by Abe, Takuro
#32S22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.15059

Abstract

We study a generalized version of Terao's famous addition theorem for free arrangements to the category of those with projective dimension one. Namely, we give a criterion to determine the algebraic structure of logarithmic derivation modules of the addition when the deletion and restrictions are free with a mild condition. Also, we introduce a class of divisionally SPOG arrangements whose SPOGness depends only on the intersection lattice like Terao's famous conjecture on combinatoriality of freeness.

Related

• Projective dimensions of hyperplane arrangements
• Addition-deletion theorem for free hyperplane arrangements and combinatorics
• Derivation degree sequences of non-free arrangements
• Freeness and near freeness are combinatorial for line arrangements in small degrees
• Plus-one generated and next to free arrangements of hyperplanes