English

Free, not recursively free and non rigid arrangements

Combinatorics 2014-06-30 v2 Algebraic Geometry

Abstract

We construct counterexamples to Yoshinaga's conjecture that every free arrangement is either inductively free or rigid in characteristic zero. The smallest example has 1313 hyperplanes, its intersection lattice has a one dimensional moduli space, and it is free but not recursively free.

Keywords

Cite

@article{arxiv.1406.6154,
  title  = {Free, not recursively free and non rigid arrangements},
  author = {Michael Cuntz},
  journal= {arXiv preprint arXiv:1406.6154},
  year   = {2014}
}

Comments

After posting the first version of this paper, I was informed by Professor Takuro Abe that Abe, Kawanoue, and Nozawa also found the arrangement with 13 hyperplanes independently, see arXiv:1406.5820. 9 pages, 2 figures