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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