On the connectivity of the realization spaces of line arrangements
Shaheen Nazir, Masahiko Yoshinaga
TL;DR
This paper investigates the connectivity of realization spaces of line arrangements in the complex projective plane, establishing conditions for connectedness and providing examples of disconnected cases.
Contribution
It introduces combinatorial conditions for connected realization spaces and presents explicit examples of arrangements with disconnected spaces.
Findings
Connected realization spaces under certain conditions
Examples of arrangements with disconnected realization spaces
Analysis of line arrangements with up to ten lines
Abstract
We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines which have disconnected realization spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Coding theory and cryptography