Thue equations over $\mathbb{C}(T)$: The Complete Solution of a Simple quartic family

Abstract

In this paper we completely solve a simple quartic family of Thue equations over C(T ). Specifically, we apply the ABC-Theorem to find all solutions (x, y) ∈ C[T ]×C [T ] to the set of Thue equations F λ (X, Y ) = ξ, where ξ ∈ C × anddenotes a family of quartic simple forms.