Free, not recursively free and non rigid arrangements

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 $13$ hyperplanes, its intersection lattice has a one dimensional moduli space, and it is free but not recursively free.

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

References in corpus (1)

• The smallest line arrangement which is free but not recursively free

Cited by in corpus (2)

• Non-recursive freeness and non-rigidity of plane arrangements
• The smallest line arrangement which is free but not recursively free