Heavy hyperplanes in multiarrangements and their freeness

Abstract

Only few categories of free arrangements are known in which Terao's conjecture holds. One of such categories consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga's freeness criterion, to unbalanced multiarrangements.

Free multiplicities on the moduli of X3

“…Figure 1. A projective picture of the X 3 arrangement labeled with multiplicities and its associated matroid diagram (1) In [6] Abe, Yoshinaga, and Terao show that the only arrangements with the property that all multiplicities are free are products of one or two dimensional arrangements. (2) In [22] Yoshinaga shows that generic arrangements have no free multiplicities.…”