A geometric condition for a hyperplane arrangement to be free
This paper collects and studies examples of arrangements obained by deleting ``few'' hyperplanes from a supersolvable (or even modularly complemented) hyperplane arrangement. Such a subarrangement can be free (in the sense of Terao) only if its characteristic polynomial factors over \({\mathbf Z}\). However, there are also many examples of non-free arrangements for which the characteristic polynomial factors. An effective method for proving non-freeness is to embed into a supersolvable arrangement and then to compare exponents in view of ``Tugger's condition''; compare the ``supersolvable resolutions'' of \textit{G. M. Ziegler} [Matroid representations and free arrangements, Trans. Am. Math. Soc. 320, No. 2, 525-541 (1990; Zbl 0727.05019)].
scientific article; zbMATH DE number 1211556
scientific article