Hyperelliptic plane curves of type (d,d-2)

TL;DR

This paper extends the classification of rational plane curves of type (d,d-2) to include irreducible curves with positive genus, broadening the understanding of their geometric properties.

Contribution

It generalizes previous classifications from rational to positive genus irreducible plane curves of the same type.

Findings

Extended classification to positive genus curves

Constructed explicit examples of such curves

Analyzed geometric properties of the generalized curves

Abstract

In a previous paper, we classified and constructed all rational plane curves of type (d,d-2). In this paper, we generalize these results to irreducible plane curves of type (d,d-2) with positive genus.