Characteristic polynomials, $η$-complexes and freeness of tame arrangements

Takuro Abe

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arXiv · 1109.1042

Characteristic polynomials, $η$-complexes and freeness of tame arrangements

Takuro Abe

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Abstract

We compare each coefficient of the reduced characteristic polynomial of a simple arrangement and that of its Ziegler restriction. As a consequence we can show that the former is not less than the latter in the category of tame arrangements. This is a generalization of Yoshinaga's freeness criterion for 3-arrangements and also the recent result by the author and Yoshinaga. As a corollary, we can prove that a free arrangement is a minimal chamber arrangement, and we can give a freeness criterion in terms of chambers in the category of tame arrangements.

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Takuro Abe. 2011-09-06. Characteristic polynomials, $η$-complexes and freeness of tame arrangements. https://arxiv.org/abs/1109.1042

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