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

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.