Abstract
We use the Kempf-Lascoux-Weyman geometric technique in order to determine the minimal free resolutions of some orbit closures of quivers. As a consequence, we obtain that for Dynkin quivers orbit closures of 1-step representations are normal with rational singularities. For Dynkin quivers of type A \mathbb {A} , we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type A \mathbb {A} quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.
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