Free resolutions of orbit closures of Dynkin quivers

Lőrincz, András; Weyman, Jerzy

doi:10.1090/tran/7697

Free resolutions of orbit closures of Dynkin quivers
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by András C. Lőrincz and Jerzy Weyman PDF

Trans. Amer. Math. Soc. 372 (2019), 2715-2734 Request permission

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 $\mathbb {A}$, we describe explicit minimal generators of the defining ideals of orbit closures of 1-step representations. Using this, we provide an algorithm for type $\mathbb {A}$ quivers for describing an efficient set of generators of the defining ideal of the orbit closure of any representation.

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