Cluster fans, stability conditions, and domains of semi-invariants
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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.References
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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
- Received by editor(s): March 5, 2009
- Received by editor(s) in revised form: August 17, 2009
- Published electronically: November 9, 2010
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 2171-2190
- MSC (2000): Primary 16G20; Secondary 05E15
- DOI: https://doi.org/10.1090/S0002-9947-2010-05184-0
- MathSciNet review: 2746679