Séminaire Lotharingien de Combinatoire, 80B.96 (2018), 12 pp.
Gleb Koshevoy
Cluster Fan of z-Vectors and Toric Degenerations
Abstract.
For a cluster algebra, we introduce and study a notion of z-vectors.
We prove that z-vectors determine cluster variables. We
associate to a cluster seed a simplicial cone being span by
z-vectors of the cluster variables of this seed. These cones form a
fan, a polyhedral complex, such that the dual graph of this complex is
the Fomin-Zelevinsky exchange graph of the cluster algebra.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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