2017/05/08 by Hoge, Torsten, Roehrle, Gerhard
#14N20 #20F55 #32S22 #51D20 #51F15 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1705.02767
Let A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A'' of A to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger freeness property of inductive freeness for these canonical free multiarrangements and investigate them for the underlying class of reflection arrangements. More precisely, let A = A(W) be the reflection arrangement of a complex reflection group W. By work of Terao, each such reflection arrangement is free. Thus so is Ziegler's canonical multiplicity on the restriction A'' of A to a hyperplane. We show that the latter is inductively free as a multiarrangement if and only if A'' itself is inductively free.