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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cluster fans, stability conditions, and domains of semi-invariants


Author: Calin Chindris
Journal: Trans. Amer. Math. Soc. 363 (2011), 2171-2190
MSC (2000): Primary 16G20; Secondary 05E15
Published electronically: November 9, 2010
MathSciNet review: 2746679
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Abstract: We show that the cone of finite stability conditions of a quiver $ Q$ without oriented cycles has a fan covering given by (the dual of) the cluster fan of $ Q$. Along the way, we give new proofs of Schofield's results (1991) on perpendicular categories. From our results, we recover Igusa-Orr-Todorov-Weyman's theorem on cluster complexes and domains of semi-invariants for Dynkin quivers. For arbitrary quivers, we also give a description of the domains of semi-invariants labeled by real Schur roots in terms of quiver exceptional sets.


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Additional Information

Calin Chindris
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: calin-chindris@uiowa.edu, chindrisc@missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05184-0
PII: S 0002-9947(2010)05184-0
Keywords: Clusters, domains of semi-invariants, exceptional sequences, stability
Received by editor(s): March 5, 2009
Received by editor(s) in revised form: August 17, 2009
Published electronically: November 9, 2010
Article copyright: © Copyright 2010 American Mathematical Society