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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

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

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