English

On the extendability of free multiarrangements

Combinatorics 2008-04-28 v3 Commutative Algebra

Abstract

A free multiarrangement of rank kk is defined to be extendable if it is obtained from a simple rank (k+1)(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.

Keywords

Cite

@article{arxiv.0710.5044,
  title  = {On the extendability of free multiarrangements},
  author = {Masahiko Yoshinaga},
  journal= {arXiv preprint arXiv:0710.5044},
  year   = {2008}
}

Comments

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"

R2 v1 2026-06-21T09:36:46.939Z