Characteristic polynomials, \(\eta \)-complexes and freeness of tame arrangements (Q1951495)

Let \(\mathcal A\) be a central arrangement of hyperplanes in an \(\ell\)-dimensional vector space. A multiarrangement occurs naturally when one restricts a central arrangement onto a hyperplane \(H_0\in \mathcal A\). In particular, the Ziegler restriction \(({\mathcal A}'', m)\) with respect to \(H_0\) is the multiarrangement defined by \({\mathcal A}'' :=\{H \cap H_0\mid H \in {\mathcal A}\setminus\{H_0\}\}\) and \(m(H\cap H_0) :=|\{K\in {\mathcal A}\setminus\{H_0\}\mid K\cap H_0 = H\cap H_0\}|\). For the case that \(\mathcal A\) and \({\mathcal A}''\) are both tame, the author attains interesting results which relate the combinatorially defined reduced characteristic polynomial of \(\mathcal A\) to the algebraically defined characteristic polynomial of \({\mathcal A}''\).