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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Free resolutions of orbit closures of Dynkin quivers


Authors: András C. Lőrincz and Jerzy Weyman
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 13D02, 14M12, 16G20; Secondary 14B05, 14M05, 14M15
DOI: https://doi.org/10.1090/tran/7697
Published electronically: May 7, 2019
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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 $ \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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Additional Information

András C. Lőrincz
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Jerzy Weyman
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

DOI: https://doi.org/10.1090/tran/7697
Received by editor(s): June 13, 2018
Published electronically: May 7, 2019
Additional Notes: The second author acknowledges the support of the National Science Foundation Grant No. 1802067.
Article copyright: © Copyright 2019 American Mathematical Society