Moduli Spaces of One-Line Extensions of (10₃) Configurations

2022/08/25 by Moshe Cohen, Cohen, Moshe, Baian Liu +1
Computer Science · Engineering · Mathematics · #14H37 #14N20 #14Q05 #32S22 #52C35 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2208.12293

openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two line arrangements in \mathbbCP² can have different topological properties even if they are combinatorially isomorphic. Results by Dan Cohen and Suciu and by Randell show that a reducible moduli space under complex conjugation is a necessary condition. We present a method to produce many examples of combinatorial line arrangements with a reducible moduli space obtained from a set of examples with irreducible moduli spaces. In this paper, we determine the reducibility of the moduli spaces of a family of arrangements of 11 lines constructed by adding a line to one of the ten (10₃) configurations. Out of the four hundred ninety-five combinatorial line arrangements in this family, ninety-five have a reducible moduli space, seventy-six of which are still reducible after the quotient by complex conjugation.

Related

• Moduli Spaces of Arrangements of 10 Projective Lines with Quadruple Points
• Connectedness and combinatorial interplay in the moduli space of line arrangements
• Moduli spaces of arrangements of 12 projective lines with a sextic point
• On the non-connectivity of moduli spaces of arrangements: the splitting-polygon structure
• Moduli spaces of ten-line arrangements with double and triple points