47 citations · 270 across the 59 of their papers we have counts for
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Addition-deletion theorem for free hyperplane arrangements and combinatorics
Takuro Abe
In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this atricle, we prove that Terao's cel…
A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
Takuro Abe, Gerhard Röhrle, Christian Stump +1
Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement…
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…