47 citations · 270 across the 59 of their papers we have counts for
6 papers · 1 filter
Non-recursive freeness and non-rigidity of plane arrangements
Takuro Abe, Michael Cuntz, Hiraku Kawanoue +1
In the category of free arrangements, inductively and recursively free arrangements are important. In particular, in the former, Terao's open problem asking whether freeness depend…
The freeness of Ish arrangements
Takuro Abe, Daisuke Suyama, Shuhei Tsujie
The Ish arrangement was introduced by Armstrong to give a new interpretation of the -Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some str…
The smallest line arrangement which is free but not recursively free
Takuro Abe, Hiraku Kawanoue, Takeshi Nozawa
In the category of free arrangements, inductively and recursively free arrangements are important. In particular, in the former, the conjecture by Terao asserting that freeness dep…
Logarithmic bundles of deformed Weyl arrangements of type
Takuro Abe, Daniele Faenzi, Jean Vallès
We consider deformations of the Weyl arrangement of type , which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their s…
Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
Takuro Abe, Hiroaki Terao
In this article we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual-partition formula. Then it immediately follows that there…
A basis construction of the extended Catalan and Shi arrangements of the type
Takuro Abe, Daisuke Suyama
In [9], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method…