Logarithmic derivations associated to line arrangements
Combinatorics
2023-12-18 v3
Abstract
In this paper we give full classification of rank 3 line arrangements in (over a field of characteristic 0) that have a minimal logarithmic derivation of degree 3. The classification presents their defining polynomials, up to a change of variables, with their corresponding affine pictures. We also analyze the shape of such a logarithmic derivation, towards obtaining criteria for a line arrangement to possess a cubic minimal logarithmic derivation.
Cite
@article{arxiv.2005.14367,
title = {Logarithmic derivations associated to line arrangements},
author = {Ricardo Burity and Stefan Tohaneanu},
journal= {arXiv preprint arXiv:2005.14367},
year = {2023}
}
Comments
18 pages, 19 pictures of line arrangements, 1 picture of articulated graph. We are very grateful to Wayne Ng Kwing King and Jean Valles for pointing to us the missing case (Vc) in Theorem 2.6. This version is about including this missing case