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

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

2008-11-08

arxiv.org/abs/0811.1290v2

Mathematics

Representation Theory

Fixed typos, minor improvements. Final version, to appear in Trans. Amer. Math. Soc

Scientific paper

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 on perpendicular categories. We also study domains of semi-invariants of quivers via quiver exceptional sequences. In particular, we recover Igusa-Orr-Todorov-Weyman's theorem on cluster complexes and domains of semi-invariants for Dynkin quivers.

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