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On the invariant theory for acyclic gentle algebras


Authors: Andrew T. Carroll and Calin Chindris
Journal: Trans. Amer. Math. Soc. 367 (2015), 3481-3508
MSC (2010): Primary 16G10, 16G60, 16R30
DOI: https://doi.org/10.1090/S0002-9947-2014-06191-6
Published electronically: December 22, 2014
MathSciNet review: 3314814
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Abstract: In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational invariants a transcendence basis in terms of Schofield's determinantal semi-invariants.

We also show that moduli spaces of modules over regular irreducible components are just products of projective spaces.


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Additional Information

Andrew T. Carroll
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Address at time of publication: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
Email: carrollat@missouri.edu, acarro15@depaul.edu

Calin Chindris
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: chindrisc@missouri.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06191-6
Keywords: Gentle algebras, module varieties, moduli spaces of modules, rank sequences, rational invariants, up and down graphs
Received by editor(s): October 12, 2012
Received by editor(s) in revised form: May 10, 2013, and May 18, 2013
Published electronically: December 22, 2014
Additional Notes: The second author was supported by NSF grant DMS-1101383
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.