On the invariant theory for acyclic gentle algebras

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In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational invariants a transcendence basis in terms of Schofield’s determinantal semi-invariants. We also show that moduli spaces of modules over regular irreducible components are just products of projective spaces.