Free resolutions of orbit closures of Dynkin quivers

Free resolutions of orbit closures of Dynkin quivers

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...

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Hauptverfasser: Lőrincz, András C, Weyman, Jerzy
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Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Mathematics - Representation Theory
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Weyman, Jerzy
description 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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subjects Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Mathematics - Representation Theory
title Free resolutions of orbit closures of Dynkin quivers
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