Abstract

In this note, we consider when a plane curve given by a polynomial of the form x3+a1(t)x2+a2(t)x+a3(t)=0, where degt ai(t)≤id(d: even), has degenerated (2,3) torus decompositions by using arithmetic properties of elliptic surfaces and show that a 3-cuspidal quartic has infinitely many degenerated (2,3) torus decompositions.

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