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.References
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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
- MR Author ID: 182230
- ORCID: 0000-0003-1923-0060
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 2715-2734
- MSC (2010): Primary 13D02, 14M12, 16G20; Secondary 14B05, 14M05, 14M15
- DOI: https://doi.org/10.1090/tran/7697
- MathSciNet review: 3988590