A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions

Takuro Abe, Norihiro Nakashima

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)585-599
Number of pages15
JournalAlgebras and Representation Theory
Volume24
Issue number3
DOIs
Publication statusPublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics

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