Moduli space of Higgs coherent systems with stable underlying vector bundles over a curve

Let X be a smooth, connected complex projective curve of genus at least 2. A Higgs coherent system is defined as an augmented bundle (E, V), where E is a holomorphic vector bundle over X, and V is a linear subspace of the space of Higgs fields of E. The purpose of this paper is twofold. First, we introduce the moduli problem of Higgs coherent systems over X. Second, we construct the fine moduli space for Higgs coherent systems with stable underlying vector bundles. The construction is achieved by establishing the representability of the associated moduli functor by a projective scheme together with a universal family.