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.Comment: 23 pages; v2 minor changes; final version, to appear in J. Algebr