On (2,3) torus decompositions of QL-configurations

TL;DR

This paper proves the existence and near-uniqueness of a specific (2,3) torus decomposition for affine quartic curves that do not intersect transversely with the line at infinity.

Contribution

It establishes the existence of a (2,3) torus decomposition for a class of affine quartic curves and proves its uniqueness except for one class.

Findings

Existence of (2,3) torus decomposition for certain affine quartics

Uniqueness of the decomposition except for one class

Advances understanding of polynomial decompositions of algebraic curves

Abstract

Let $Q$ be an affine quartic which does not intersect transversely with the line at infinity $L_{\infty}$. In this paper, we show the existence of a $(2,3)$ torus decomposition of the defining polynomial of $Q$ and its uniqueness except for one class.