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On the projective dimension of some deformations of Weyl arrangements
Takuro Abe, Daniele Faenzi
We show that the logarithmic derivation module of (the cone of) the deformation A of a Weyl arrangement associated with a root system of simply laced type has projective dimension…
A new hierarchy for complex plane curves
Takuro Abe, Alexandru Dimca, Piotr Pokora
We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Cu…
Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements
Takuro Abe
The Solomon-Terao bi-polynomial was introduced by Solomon and Terao which degenerates to the characteristic polynomial of hyperplane arrangements. Also, it was proved recently that…
Tame arrangements
Takuro Abe
Tame arrangements were informally introduced by Orlik and Terao for the study of Milnor fibers of hyperplane arrangements. After that, tame arrangements have been applied to a lot…