Resolutions of defining ideals of orbit closures for quivers of type A3
Abstract
We investigate the properties of coordinate rings of orbit closures for quivers of type A3 by considering the desingularization given by Reineke. We construct explicit minimal free resolutions of the defining ideals of the orbit closures thus giving us a minimal set of generators for the defining ideal. The resolution allows us to read off some geometric properties of the orbit closure. In addition, we give a characterization for the orbit closure to be Gorenstein.
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