Moduli of Higgs Coherent Systems with stable underlying vector bundles over a curve

TL;DR

This paper introduces the moduli space of Higgs coherent systems on a complex curve, focusing on systems with stable underlying bundles, and constructs a fine moduli space for these systems.

Contribution

It defines the moduli problem for Higgs coherent systems and constructs the fine moduli space for systems with stable underlying bundles.

Findings

Defined the moduli problem for Higgs coherent systems

Constructed the fine moduli space for stable underlying bundles

Established foundational results for Higgs coherent systems on curves

Abstract

Let $X$ be a smooth, connected complex projective curve of genus at least $2$. A Higgs coherent system is an augmented bundle $(E,V)$, where $E$ is a holomorphic vector bundle, and $V$ is a linear subspace of the spaces of Higgs bundles 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.