47 citations · 270 across the 59 of their papers we have counts for
10 papers · 1 filter
Locally Heavy Hyperplanes in Multiarrangements
Takuro Abe, Lukas Kühne
Hyperplane Arrangements of rank admitting an unbalanced Ziegler restriction are known to fulfill Terao's conjecture. This long-standing conjecture asks whether the freeness of…
Plus-one generated and next to free arrangements of hyperplanes
Takuro Abe
We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freenes…
Solomon-Terao algebra of hyperplane arrangements
Takuro Abe, Toshiaki Maeno, Satoshi Murai +1
We introduce a new algebra associated with a hyperplane arrangement , called the Solomon-Terao algebra $\mbox{ST}(\mathcal{A},η)$, where is a homogeneous polynomia…
Restrictions of free arrangements and the division theorem
Takuro Abe
This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in [2]. The division theorem is a generalization of classical addit…
Divisionally free arrangements of hyperplanes
Takuro Abe
We consider the triple of hyperplane arrangements and the division of their characteristic polynomials. We show that the freeness of $\ma…
Exponents of 2-multiarrangements and freeness of 3-arrangements
Takuro Abe
We give the upper bound of differences of exponents for balanced 2-multiarrangements in terms of the cardinality of hyperplanes. Also, we give a shift isomorphism of 2-multiarrange…