  An m-free hyperplane arrangement is a generalization of a free arrangement.
Holm asked the following two questions: (1)Does m-free imply (m+1)-free for any
arrangement? (2)Are all arrangements m-free for m large enough? In this paper,
we characterize m-freeness for product arrangements, while we prove that all
localizations of an m-free arrangement are m-free. From these results, we give
answers to Holm's questions.
