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We give a moduli-theoretic treatment of the existence and properties ofmoduli spaces of semistable quiver representations, avoiding methods fromgeometric invariant theory. Using the existence criteria ofAlper--Halpern-Leistner--Heinloth, we show that for many stability functions,the stack of semistable representations admits an adequate moduli space, andprove that this moduli space is proper over the moduli space of semisimplerepresentations. We construct a natural determinantal line bundle that descendsto a semiample line bundle on the moduli space and provide new effective boundsfor global generation. For an acyclic quiver, we show that this line bundle isample, thus giving a modern proof of the fact that the moduli space isprojective.

Projectivity and effective global generation of determinantal line bundles on quiver moduli