Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations

2021/06/24 by Abe, Takuro
#32S22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.12756

Abstract

Terao's factorization theorem shows that if an arrangement is free, then its characteristic polynomial factors into the product of linear polynomials over the integer ring. This is not a necessary condition, but there are not so many non-free arrangements whose characteristic polynomial factors over the integer ring. On the other hand, the localization of a free arrangement is free, and its restriction is in many cases free, thus its characteristic polynomial factors. In this paper, we consider how their integer, or real roots behave.

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