Recent results on quiver sheaves
The authors survey recent work on quiver sheaves, that is (twisted) representations of quivers in the category of coherent sheaves on a projective algebraic variety \(X\). Allowing the twisting means in particular that Higgs bundles are included as an example. A preliminary section on quiver representations, that is representations of quivers in the category of finite dimensional complex vector spaces, is followed by a section on quivers, sheaves and instantons. After that, the authors move on to quiver sheaves and, in particular, stability conditions for such sheaves. This includes an extended discussion for the quiver \(\bullet\longleftarrow\bullet\longrightarrow\bullet\), where the authors present some new results. The paper is completed with a short section on Higgs bundles, which have of course been extensively studied in recent years.
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