On the extendability of free multiarrangements

Details On the extendability of free multiarrangements On the extendability of free multiarrangements

2007-10-26

arxiv.org/abs/0710.5044v3

Mathematics

Combinatorics

7 pages, v2: errors corrected and expanded, v3: errors corrected. To appear in the proceeding of 2007 CIMPA Summer School "Arr

Scientific paper

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.

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