Divisionally free arrangements of hyperplanes

Takuro Abe

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


Let (Formula presented.) be the triple of hyperplane arrangements. We show that the freeness of (Formula presented.) and the division of (Formula presented.) by (Formula presented.) imply the freeness of (Formula presented.). This “division theorem” improves the famous addition–deletion theorem, and it has several applications, which include a definition of “divisionally free arrangements”. It is a strictly larger class of free arrangements than the classical important class of inductively free arrangements. Also, whether an arrangement is divisionally free or not is determined by the combinatorics. Moreover, we show that a lot of recursively free arrangements, to which almost all known free arrangements are belonging, are divisionally free.

Original languageEnglish
Pages (from-to)317-346
Number of pages30
JournalInventiones Mathematicae
Issue number1
Publication statusPublished - Apr 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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