In Section 4 of the paper Kirwan surjectivity for quiver varieties (Inventiones Math. 2018) McGerty and Nevins define a compactification of the moduli space of representations of the preprojective algebra associated to a quiver as the moduli space of representations of another quiver (the "tripling" of the original quiver) with certain relations. This compactification plays a key role in this paper and is defined by an explicit procedure obtaining the vertices and edges for the "tripled" quiver starting with the vertices and edges of the original quiver. My question is: what is the intuition behind the definition of such a compactification? Are there other constructions of (modular) compactifications of quiver varieties?

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