Group-labeled light dual multinets in the projective plane (with Appendix)

TL;DR

This paper studies group-labeled light dual multinets in projective planes over fields, introduces new examples, and classifies certain configurations under specific conditions on the field's characteristic.

Contribution

It presents two new classes of light dual multinets and provides a classification for those with lines of length at least 9 under certain field conditions.

Findings

Two new classes of light dual multinets are constructed.

Classification of group-labeled light dual multinets with lines of length ≥ 9.

Results depend on conditions related to the characteristic of the field.

Abstract

In this paper we investigate light dual multinets labeled by a finite group in the projective plane $PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$. We present two classes of new examples. Moreover, under some conditions on the characteristic $\mathbb{K}$, we classify group-labeled light dual multinets with lines of length least $9$.