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arXiv · 1801.00193

Free resolutions of orbit closures of Dynkin quivers

András C. Lőrincz·Jerzy Weyman
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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 $A$, we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type $A$ quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.

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András C. Lőrincz, Jerzy Weyman. 2017-12-30. Free resolutions of orbit closures of Dynkin quivers. https://arxiv.org/abs/1801.00193

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