On $3$-syzygy and unexpected plane curves

TL;DR

This paper investigates special arrangements of curves in the complex projective plane, focusing on nearly free and 3-syzygy arrangements, and presents examples with unexpected geometric properties.

Contribution

It introduces new families of nearly free arrangements and explores 3-syzygy arrangements with unexpected curves, expanding understanding of curve arrangements in algebraic geometry.

Findings

Constructed nearly free arrangements with interesting properties

Presented examples of 3-syzygy arrangements with unexpected curves

Enhanced understanding of geometric properties of complex plane curves

Abstract

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study $3$-syzygy arrangements and we present examples that admit unexpected curves.