Curves with rational families of quasi-toric relations

TL;DR

This paper studies plane curves that have rational families of quasi-toric relations, extending earlier results to both positive and negative cases, thereby broadening understanding of these geometric structures.

Contribution

It generalizes previous work by characterizing plane curves with rational quasi-toric relations in both positive and negative cases.

Findings

Extended classification of plane curves with rational quasi-toric relations.

Unified approach for positive and negative cases.

Broadened the theoretical framework for quasi-toric relations.

Abstract

We investigate which plane curves admit rational families of quasi-toric relations. This extends previous results of Takahashi and Tokunaga in the positive case and of the author in the negative case.