On $(4,3)$ line degenerated torus curves and torus decompositions

Abstract

Let $C = \{f = 0\}$ be an affine plane curve. In this paper, we study $(4,3)$ line degenerations of torus curves. Line degenerations of torus curves are divided into two types which are called visible or invisible degenerations. We will show that there does not exist a $(4,3)$ line degenerated torus curve which has two types decompositions.