Free line arrangements with low maximal multiplicity
Abstract
Let $${\mathcal {A}}$$ be a free arrangement of d lines in the complex projective plane, with exponents $$d_1\le d_2$$ . Let m be the maximal multiplicity of points in $${\mathcal {A}}$$ . In this note, we describe first the simple cases $$d_1 \le m$$ . Then, we study the case $$d_1=m+1$$ and describe which line arrangements can occur by deleting or adding a line to $${\mathcal {A}}$$ . When $$d \le 14$$ , there are only two free arrangements with $$d_1=m+2$$ , namely one with degree 13 and the other with degree 14. We study their geometries in order to deepen our understanding of the structure of free line arrangements in general.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Algebraic Geometry and Number Theory
Tensor decomposition and applications
Publication details
- Journal / source
- Journal of Algebraic Combinatorics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 63
- Issue
- 3
- Publication date
- 1 May 2026
- Language
- EN