On type three complex plane curves

TL;DR

This paper investigates complex projective plane curves of type three, focusing on low degree cases and line arrangements, expanding the understanding of their classification and properties.

Contribution

It introduces a detailed study of type three curves, particularly low degree and line arrangements, building on previous work on types one and two.

Findings

Classification of low degree type three curves

Analysis of line arrangements of type three

Extension of the type classification framework

Abstract

The type of a complex projective plane curve has been recently introduced by T. Abe, P. Pokora and the first author. In the same paper they have studied the type two curves. In this paper we study plane curves of type three, with special attention to low degree curves and line arrangements.