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arXiv · 1705.07417

A characterization of high order freeness for product arrangements and answers to Holm's questions

Takuro Abe·Norihiro Nakashima
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Abstract

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.

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Takuro Abe, Norihiro Nakashima. 2017-10-30. A characterization of high order freeness for product arrangements and answers to Holm's questions. https://arxiv.org/abs/1705.07417

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