TY - JOUR
T1 - A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions
AU - Abe, Takuro
AU - Nakashima, Norihiro
N1 - Funding Information:
The authors would like to thank Noriyuki Abe and Mutsumi Saito for useful discussions about the proof of Claim 4.10. The first author is partially supported by JSPS Grant-in-Aid for Scientific Research (B) 16H03924, and Grant-in-Aid for Exploratory Research 16K13744. The second author is supported by JSPS Grant-in-Aid for Young Scientists (B) 16K17582.
Publisher Copyright:
© 2020, Springer Nature B.V.
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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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U2 - 10.1007/s10468-020-09961-1
DO - 10.1007/s10468-020-09961-1
M3 - Article
AN - SCOPUS:85084635975
SN - 1386-923X
VL - 24
SP - 585
EP - 599
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 3
ER -