On $3$-syzygy and unexpected 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.

19 pages, one figure, version after referee's remarks

Cited by in corpus (3)

• On plane conic arrangements with nodes and tacnodes
• On Poincaré polynomials for plane curves with quasi-homogeneous singularities
• On free and nearly free arrangements of conics admitting certain $\mathrm{ADE}$ singularities