On the extendability of free multiarrangements
Abstract
Description
A free multiarrangement of rank $k$ is defined to be extendable if it is obtained from a simple rank $(k+1)$ free arrangement by the natural restriction to a hyperplane (in the sense of Ziegler). Not all free multiarrangements are extendable. We will discuss extendability of free multiarrangements for a special class. We also give two applications. The first is to produce totally non-free arrangements. The second is to give interpolating free arrangements between extended Shi and Catalan arrangements.
7 pages, v2: errors corrected and expanded, v3: errors corrected. To appear in the proceeding of 2007 CIMPA Summer School "Arrangements, Local systems and Singularities"
7 pages, v2: errors corrected and expanded, v3: errors corrected. To appear in the proceeding of 2007 CIMPA Summer School "Arrangements, Local systems and Singularities"