Resolutions of defining ideals of orbit closures for quivers of type $A_3$

Details Resolutions of defining ideals of orbit closures for quivers of type $A_3$ Resolutions of defining ideals of orbit closures for quivers of type $A_3$

2011-11-04

arxiv.org/abs/1111.1179v1

Mathematics

Algebraic Geometry

20 pages, 6 figures

Scientific paper

We investigate the properties of coordinate rings of orbit closures for quivers of type $A_3$ 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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