Inductive and Recursive Freeness of Localizations of Multiarrangements

Abstract

The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are compatible with the product construction for multiarrangements. In addition, we show how our results can be used to derive that some canonical classes of free multiarrangements are not inductively free.

17 pages; v 2: introductory material slightly rearranged, some references added and updated; acknowledged grant support, 16 pages;